I have successfully setup my Pleroma instance with GarageHQ and would share this in the documentation.
The part with the loop is totally optionnal, but, as I said, in case of old link in Pleroma database I prefer run it.
Reviewed-on: https://git.deuxfleurs.fr/Deuxfleurs/garage/pulls/1294
Co-authored-by: Dryusdan <contact@dryusdan.fr>
Co-committed-by: Dryusdan <contact@dryusdan.fr>
Put the features flags into alphabetical order in both the cookbook and
the version information, so that it is easier to document additional
feature flags.
The version control site was migrated from Gitea to Forgejo some time
ago, and Forgejo has declared a hard fork from Gitea[1]. Update the
documentation and links to refer to the site as a Forgejo instance
instead of a Gitea instance.
[1] https://forgejo.org/2024-02-forking-forward/
Buypass Go SSL has stopped providing SSL/TLS certificates, including
from their ACME API endpoints, as of October 2025, and the service is to
be completely phased out by April 2026:
https://community.buypass.com/t/y4y130p
Remove them from the docs as an ACME-capable provider.
When not used. Especially with a lot of small files on the PVC's Garage uses/is configured with,
Pod upstart time can get quite extreme. For more context see a very good description
of the issues and the technical intricacies behind it here: https://github.com/longhorn/longhorn/issues/2131#issuecomment-778897129
I think it's sane to have fsGroupChangePolicy at "OnRootMismatch" as Garage is an S3 system and thereby
is likely to process a lot of files. And somewhat likely that many of these will be small files as well.
---
Using `fsGroupChangePolicy: "OnRootMismatch"` in my env. changed the Garage Pod upstart. E.g. in an
upgrade case from 5-7minutes ( around 50GB of data ). Many small files though. To 1-15sec.
Thank you.
Signed-off-by: larssb <larssb@noreply.localhost>
The systemd-journald is used in most major Linux distros that use systemd.
This enables logging using the systemd-journald native protocol, instead
of just writing to stderr.
i went with a `500`/`InternalError`/`Please try again.` because that is something i've seen AWS S3 report while developing other software, and i'm not convinced all clients would understand a 409 conflict properly (GET don't usually conflict)
Reviewed-on: https://git.deuxfleurs.fr/Deuxfleurs/garage/pulls/1053
Co-authored-by: trinity-1686a <trinity@deuxfleurs.fr>
Co-committed-by: trinity-1686a <trinity@deuxfleurs.fr>
- Remove the replication_factor.replication_factor() in favor of
usize::from(replication_factor) to make the conversion more explicit.
- Implement Display on ReplicationFactor so that it can be formatted
without converting to usize
- Use ReplicationFactor in the constructor of LayoutVersion and add a
method to get a ReplicationFactor from a LayoutVersion, despite
LayoutVersion still storing it as usize internally.
See #1006
LMDB files never shrink, so we can end up with a large database that
contains a smaller amount of actual data.
Compacting the snapshots is an easy win: it will write faster to disk,
take less space, and if needed you can reimport an already-compacted
snapshot as the main database.
In particular, it means that "garage meta snapshot --all" will get an exit
code of 1 if any node fails to snapshot.
This makes sure that any external tool trying to snapshot nodes (e.g. from
cron) will be aware of the failure.
Fix#920
Snapshot errors on remote nodes were not reported at all.
We now get proper error output such as:
0fa0f35be69528ab error: Internal error: DB error: LMDB: No space left on device (os error 28)
88d92e2971d14bae ok
Fix#920
admin api: rename EndpointHandler into RequestHandler to avoid confusion with RPC
wip: infrastructure for local api calls
admin api: fix things
admin api: first local endpoint to work with new scheme
admin api: implement SetWorkerVariable
This removes our dependency on cargo2nix, which was causing us some
issues. Whereas cargo2nix creates one Nix derivation per crate, Crane
uses only two derivations:
1. Build dependencies only
2. Build the final binary
This means that during the second step, no caching can be done. For
instance, if we do a change in garage_model, we need to recompile all of
the Garage crates including those that do not depend on garage_model.
On the upside, this allows all of the Garage crates to be built at once
using cargo build logic, which is optimized for high parallelism and
better pipelining between all of the steps of the build. All in all,
this makes most builds faster than cargo2nix.
A few other changes have been made to the build scripts and CI:
- Unit tests are now run within a Nix derivation. In fact, we have
different derivations to run the tests using LMDB and Sqlite as
metadata db engines.
- For debug builds, most CI steps now run in parallel (with the notable
exception of the smoke test that runs after the build, which is
inevitable).
- We no longer pass the GIT_VERSION argument when building debug builds
and running the tests. This means that dev binaries and test
binaries don't know the exact version of Garage they are from. That
shouldn't be an issue in most cases.
- The not-dynamic.sh scripts has been fixed to fail if the file does not
exist.
This change is probably not a proper fix, somebody with more expertise on
this code should look at it.
Here is how to reproduce the crash:
- start with a layout with two zones
- move all nodes of a zone to gateway mode: `garage layout assign fea54bcc081f318 -g`
- `garage layout show` will panic with a backtrace
Fortunately, the crash is only on the RPC client side, not on the Garage
server itself, and `garage layout revert` still works to go back to the
previous state.
As far as I can tell, this bug is present since Garage 0.9.0 which
includes the new layout assignation algorithm:
https://git.deuxfleurs.fr/Deuxfleurs/garage/pulls/296
Currently, taking a snapshot of the metadata database with sqlite creates
a sqlite file without extension with the following format:
snapshots/2025-01-26T15:29:17Z
This makes it hard to understand what kind of data this is, and is not
consistent with LMDB:
snapshots/2025-01-26T15:29:17Z/data.mdb
With this change, we now get a directory with a single db.sqlite file:
snapshots/2025-01-26T15:29:17Z/db.sqlite
I followed the documentation and got an error if the layout's version was not specified
```
garage layout apply
Error: Internal error:
Please pass the new layout version number to ensure that you are writing the correct version of the cluster layout.
To know the correct value of the new layout version, invoke `garage layout show` and review the proposed changes.
```
This fixes that
In case `rpc_public_addr` is not set, but autodiscovery is used, this
allows filtering the list of automatically discovered IPs to a specific
subnet.
For example, if nodes should pick *their* IP inside a specific subnet,
but you don't want to explicitly write the IP down (as it's dynamic, or
you want to share configs across nodes), you can use this option.
- We always recalculate the reference count of a block before deleting
it locally, to make sure that it is indeed zero.
- If we had to fetch a remote block but we were not able to get it,
check that refcount is indeed > 0.
- Repair procedure that checks everything
This page of the AWS docs indicate that Content-Type should be part of
the CanonicalHeaders (and therefore SignedHeaders) strings in signature
calculation:
https://docs.aws.amazon.com/AmazonS3/latest/API/sig-v4-header-based-auth.html
However, testing with Minio Client revealed that it did not sign the
Content-Type header, and therefore we broke CI by expecting it to be
signed. With this commit, we don't mandate Content-Type to be signed
anymore, for better compatibility with the ecosystem. Testing against
the official behavior of S3 on AWS has not been done.
For some users, this might be their first time being interacting with
the `env_logger` crate.
As such, they might not be aware that less verbose log levels exist.
Some might not want to log every incoming request, for example.
This commit also adds syntax hints to the code-fence for bash for better
syntax highlighting of that section, and repeats itself multiple times,
that `info` is, in fact, the default.
No changes to the recommendation of log levels were made.
Having all Engine enum variants conditional causes compilation errors
when *none* of the DB engine features is enabled. This is not an issue
for full garage build, but affects crates that use garage_db as
dependency.
Change all variants to be present at all times. It solves compilation
errors and also allows us to better differentiate between invalid DB
engine name and engine with support not compiled in current binary.
Use optional DB open overrides for both input and output database.
Duplicating the same override flag for input/output would result in too
many, too long flags. It would be too costly for very rare edge-case
where converting between same DB engine, just with different flags.
Because overrides flags for different engines are disjoint and we are
preventing conversion between same input/ouput DB engine, we can have
only one set.
The override flag will be passed either to input or output, based on
engine type it belongs to. It will never be passed to both of them and
cause unwelcome surprise to user.
Garage v0.8.5
This minor release includes the following improvements and fixes:
New features:
- Configuration: make LMDB's `map_size` configurable and make `block_size` and `sled_cache_capacity` expressable as strings (such as `10M`) (#628, #630)
- Add support for binding to Unix sockets for the S3, K2V, Admin and Web API servers (#640)
- Move the `convert_db` command into the main Garage binary (#645)
- Add support for specifying RPC secret and admin tokens as environment variables (#643)
- Add `allow_world_readable_secrets` option to config file (#663, #685)
Bug fixes:
- Use `statvfs` instead of mount list to determine free space in metadata/data directories (#611, #631)
- Add missing casts to fix 32-bit build (#632)
- Fix error when none of the HTTP servers (S3/K2V/Admin/Web) is started and fix shutdown hang (#613, #633)
- Add missing CORS headers to PostObject response (#609, #656)
- Monitoring: finer histogram boundaries in Prometheus exported metrics (#531, #686)
Other:
- Documentation improvements (#641)
Sometimes, the secret files permissions checks gets in the way. It's
by no mean complete, it doesn't take the Posix ACLs into account among
other things. Correctly checking the ACLs would be too involving (see
https://git.deuxfleurs.fr/Deuxfleurs/garage/issues/658#issuecomment-7102)
and would likely still fail in some weird chmod settings.
We're adding a new configuration file key allowing the user to disable
this permission check altogether.
The (already existing) env variable counterpart always take precedence
to this config file option. That's useful in cases where the
configuration file is static and cannot be easily altered.
Fixes https://git.deuxfleurs.fr/Deuxfleurs/garage/issues/658
Co-authored-by: Florian Klink <flokli@flokli.de>
This is still a bit confusing, as normally the flake.defaultNix attrset
gets exposed via a top-level default.nix, but at least it brings us
closer to that.
Compiling garage_db v0.8.2 (garage-0.8.2/src/db)
error: cannot find macro `warn` in this scope
--> src/db/lmdb_adapter.rs:352:2
|
352 | warn!("LMDB is not recommended on 32-bit systems, database size will be limited");
| ^^^^
|
= help: consider importing this macro:
tracing::warn
= note: `warn` is in scope, but it is an attribute: `#[warn]`
error: could not compile `garage_db` due to previous error
- self.node_id_vec was not properly updated when the previous ring was empty
- ClusterLayout::merge was not considering changes in the layout parameters
- have consistent error return types
- store the zone redundancy in a Lww
- print the error and message in the CLI (TODO: for the server Api, should msg be returned in the body response?)
It takes as paramters the replication factor and the zone redundancy, computes the
largest partition size reachable with these constraints, and among the possible
assignation with this partition size, it computes the one that moves the least number
of partitions compared to the previous assignation.
This computation uses graph algorithms defined in graph_algo.rs
The function now computes an optimal assignation (with respect to partition size) that minimizes the distance to the former assignation, using flow algorithms.
This commit was written by Mendes Oulamara <mendes.oulamara@pm.me>
2022-05-01 09:54:19 +02:00
544 changed files with 102085 additions and 22248 deletions
Nextcloud will now make Garage encrypt files at rest in the storage bucket.
These files will not be readable by an S3 client that has credentials to the
bucket but doesn't also know the secret encryption key.
### External Storage
**From the GUI.** Activate the "External storage support" app from the "Applications" page (click on your account icon on the top right corner of your screen to display the menu). Go to your parameters page (also located below your account icon). Click on external storage (or the corresponding translation in your language).
@@ -87,7 +136,7 @@ To test your new configuration, just reload your Nextcloud webpage and start sen
*Click on the picture to zoom*
Add a new external storage. Put what you want in "folder name" (eg. "shared"). Select "Amazon S3". Keep "Access Key" for the Authentication field.
In Configuration, put your bucket name (eg. nextcloud), the host (eg. 127.0.0.1), the port (eg. 3900 or 443), the region (garage). Tick the SSL box if you have put an HTTPS proxy in front of garage. You must tick the "Path access" box and you must leave the "Legacy authentication (v2)" box empty. Put your Key ID (eg. GK...) and your Secret Key in the last two input boxes. Finally click on the tick symbol on the right of your screen.
In Configuration, put your bucket name (eg. nextcloud), the host (eg. 127.0.0.1), the port (eg. 3900 or 443), the region ("garage" if you use the default, or the one your configured in your `garage.toml`). Tick the SSL box if you have put an HTTPS proxy in front of garage. You must tick the "Path access" box and you must leave the "Legacy authentication (v2)" box empty. Put your Key ID (eg. GK...) and your Secret Key in the last two input boxes. Finally click on the tick symbol on the right of your screen.
Now go to your "Files" app and a new "linked folder" has appeared with the name you chose earlier (eg. "shared").
@@ -138,15 +187,15 @@ a reasonable trade-off for some instances.
Create a key for Peertube:
```bash
garage key new --name peertube-key
garage key create peertube-key
```
Keep the Key ID and the Secret key in a pad, they will be needed later.
We need two buckets, one for normal videos (named peertube-video) and one for webtorrent videos (named peertube-playlist).
We need two buckets, one for normal videos (named peertube-videos) and one for webtorrent videos (named peertube-playlists).
```bash
garage bucket create peertube-video
garage bucket create peertube-playlist
garage bucket create peertube-videos
garage bucket create peertube-playlists
```
Now we allow our key to read and write on these buckets:
@@ -190,7 +239,7 @@ object_storage:
# Put localhost only if you have a garage instance running on that node
endpoint: 'http://localhost:3900' # or "garage.example.com" if you have TLS on port 443
# Garage supports only one region for now, named garage
# Garage default region is named "garage", edit according to your config
region: 'garage'
credentials:
@@ -205,7 +254,7 @@ object_storage:
proxify_private_files: false
streaming_playlists:
bucket_name:'peertube-playlist'
bucket_name: 'peertube-playlists'
# Keep it empty for our example
prefix: ''
@@ -215,7 +264,7 @@ object_storage:
# Same settings but for webtorrent videos
videos:
bucket_name:'peertube-video'
bucket_name: 'peertube-videos'
prefix: ''
# You must fill this field to make Peertube use our reverse proxy/website logic
Ente is an alternative for Google Photos and Apple Photos. It [can be selfhosted](https://help.ente.io/self-hosting/) and is working fine with Garage as of May 2024.
As a first step we need to create a bucket and a key for Ente:
```bash
garage bucket create ente
garage key create ente-key
# For the CORS setup to work, the key needs to be --owner as well, at least temporarily.
garage bucket allow ente --read --write --owner --key ente-key
```
We also need to setup some CORS rules to allow the Ente frontend to access the bucket:
aws s3api put-bucket-cors --bucket ente --cors-configuration $CORS
```
Now we need to configure ente-server to use our bucket. This is explained [in the Ente S3 documentation](https://help.ente.io/self-hosting/guides/external-s3).
Prepare a configuration file for ente's backend as `museum.yaml`:
```yaml
credentials-file: /credentials.yaml
apps:
public-albums: https://albums.example.tld # If you want to use the share album feature
internal:
hardcoded-ott:
local-domain-suffix: "@example.com" # Your domain
local-domain-value: 123456 # Custom One-Time Password since we are not sending mail by default
key:
# WARNING -- You MUST CHANGE the values below
# Someone has made an image that can do it for you : https://github.com/EdyTheCow/ente-selfhost/blob/main/images/ente-server-tools/Dockerfile
# Simply build it yourself or run docker run --rm ghcr.io/edythecow/ente-server-tools go run tools/gen-random-keys/main.go
encryption: yvmG/RnzKrbCb9L3mgsmoxXr9H7i2Z4qlbT0mL3ln4w= # CHANGE THIS VALUE
hash: KXYiG07wC7GIgvCSdg+WmyWdXDAn6XKYJtp/wkEU7x573+byBRAYtpTP0wwvi8i/4l37uicX1dVTUzwH3sLZyw== # CHANGE THIS VALUE
jwt:
secret: i2DecQmfGreG6q1vBj5tCokhlN41gcfS2cjOs9Po-u8= # CHANGE THIS VALUE
```
The full configuration file can be found [here](https://github.com/ente-io/ente/blob/main/server/configurations/local.yaml)
Then prepare a credentials file as `credentials.yaml`
```yaml
db:
host: postgres
port: 5432
name: <ente_db_name>
user: <pguser>
password: <pgpass>
s3:
# Override the primary and secondary hot storage. The commented out values
# are the defaults.
#
hot_storage:
primary: b2-eu-cen
# secondary: wasabi-eu-central-2-v3
# If true, enable some workarounds to allow us to use a local minio instance
# for object storage.
#
# 1. Disable SSL.
# 2. Use "path" style S3 URLs (see `use_path_style_urls` below).
# 3. Directly download the file during replication instead of going via the
# Cloudflare worker.
# 4. Do not specify storage classes when uploading objects (since minio does
# not support them, specifically it doesn't support GLACIER).
are_local_buckets: true
# To use "path" style S3 URLs instead of DNS-based bucket access
# default to true if you set "are_local_buckets: true"
# use_path_style_urls: true
b2-eu-cen: # Don't change this key, it is hardcoded
key: <keyID>
secret: <keySecret>
endpoint: garage:3900 # publically accessible endpoint of your garage instance
region: garage
bucket: <yourbucketName>
use_path_style: true
# you can specify secondary locations, names are hardcoded as well
# wasabi-eu-central-2-v3:
# scw-eu-fr-v3:
# and you can also specify a bucket to be used for embeddings, preview etc..
We also need to expose these buckets publicly to serve their content to users:
```bash
garage bucket website --allow pleroma
```
Note the Key ID and Secret Key.
### Configure Pleroma
Update your Pleroma configuration like that in `/etc/pleroma/config.exs`.
```
config :pleroma, Pleroma.Upload,
uploader: Pleroma.Uploaders.S3,
base_url: "https://pleroma.garage.example.tld"
config :ex_aws, :s3,
access_key_id: "GW...",
secret_access_key: "XXX",
region: "garage",
host: "api.garage.example.tld"
```
And restart Pleroma.
You can found more information in [Pleroma Documentation > Pleroma.Uploaders.S3](https://docs-develop.pleroma.social/backend/configuration/cheatsheet/#pleromauploaderss3)
### Migrating your data
Pleroma have an internal migration tool that can encounter some fatal error
```
** (EXIT from #PID<0.98.0>) an exception was raised:
** (File.Error) could not stream "/var/lib/pleroma/uploads/09/f8": illegal operation on a directory
(elixir 1.17.3) lib/file/stream.ex:100: anonymous fn/3 in Enumerable.File.Stream.reduce/3
(elixir 1.17.3) lib/stream.ex:1675: anonymous fn/5 in Stream.resource/3
On Plakar server, add your Garage as a storage location:
```bash
plakar store add garageS3 s3://my-garage.tld/plakar-backups \
region=garage # Or as you've specified in garage.toml \
access_key=<Key ID from "garage key info my-plakar-key"> \
secret_access_key=<Secret key from "garage key info my-plakar-key">
```
Then create the repository.
```bash
plakar at @garageS3 create -plaintext # Unencrypted
# or
plakar at @garageS3 create #encrypted
```
If you encrypt your backups (Plakar default), you will need to define a strong passphrase. Do not forget to save your password safely. It will be needed to decrypt your backups.
After the repository has been created, check that everything works as expected (that might give an empty result as no file has been added yet, but no error message):
```bash
plakar at @garageS3 check
```
Now that everything is configure, you can use Garage as your backups storage. For instance sync it with a local backup storage:
```bash
$ plakar at ~/backups sync to @garageS3
```
Or list the S3 storage content:
```bash
$ plakar at @garageS3 ls
```
More information in Plakar documentation: https://www.plakar.io/docs/main/quickstart/
## Synology HyperBackup
HyperBackup can be configured to upload backups to garage using a custom S3 destination. However, the HyperBackup client hardcodes the `us-east-1` region that is a critical input to the v4 signature process. If garage is not set to `us-east-1`, HyperBackup will recognize available buckets, but fail during the final setup stage.
@@ -70,16 +70,17 @@ Then a file named `~/.aws/config` and put:
```toml
[default]
region=garage
endpoint_url=http://127.0.0.1:3900
```
Now, supposing Garage is listening on `http://127.0.0.1:3900`, you can list your buckets with:
```bash
aws --endpoint-url http://127.0.0.1:3900 s3 ls
aws s3 ls
```
Passing the `--endpoint-url` parameter to each command is annoying but AWS developers do not provide a corresponding configuration entry.
As a workaround, you can redefine the aws command by editing the file `~/.bashrc`:
If you're using awscli `<1.29.0` or `<2.13.0`, you need to pass `--endpoint-url` to each CLI invocation explicitly.
As a workaround, you can redefine the aws command by editing the file `~/.bashrc` in this case:
```
function aws { command aws --endpoint-url http://127.0.0.1:3900 $@ ; }
@@ -148,6 +149,15 @@ rclone help
This will tremendously accelerate operations such as `rclone sync` or `rclone ncdu` by reducing the number
of ListObjects calls that are made.
**Garage behind Cloudflare proxy:** when running Garage behind Cloudflare proxy, you might see `Response: error 403 Forbidden, Forbidden: Invalid signature` error in your garage logs or `AccessDenied: Forbidden: Invalid signature` error in rclone logs. Try adding `--s3-sign-accept-encoding=false` flag to your rclone command and see if the issue is resolved.
@@ -17,13 +17,13 @@ Garage can also help you serve this content.
## Gitea
You can use Garage with Gitea to store your [git LFS](https://git-lfs.github.com/) data, your users' avatar, and their attachements.
You can use Garage with Gitea to store your [git LFS](https://git-lfs.github.com/) data, your users' avatar, and their attachments.
You can configure a different target for each data type (check `[lfs]` and `[attachment]` sections of the Gitea documentation) and you can provide a default one through the `[storage]` section.
Let's start by creating a key and a bucket (your key id and secret will be needed later, keep them somewhere):
which contains all of the released versions as well as the code
for the developpement of the next version.
@@ -85,11 +85,14 @@ The following feature flags are available in v0.8.0:
| Feature flag | Enabled | Description |
| ------------ | ------- | ----------- |
| `bundled-libs` | *by default* | Use bundled version of sqlite3, zstd, lmdb and libsodium |
| `system-libs` | optional | Use system version of sqlite3, zstd, lmdb and libsodium<br>if available (exclusive with `bundled-libs`, build using<br>`cargo build --no-default-features --features system-libs`) |
| `consul-discovery` | optional | Enable automatic registration and discovery<br>of cluster nodes through the Consul API |
| `fjall` | experimental | Enable using Fjall to store Garage's metadata |
| `journald` | optional | Enable logging to systemd-journald with<br>`GARAGE_LOG_TO_JOURNALD=true` environment variable set |
| `k2v` | optional | Enable the experimental K2V API (if used, all nodes on your<br>Garage cluster must have it enabled as well) |
| `kubernetes-discovery` | optional | Enable automatic registration and discovery<br>of cluster nodes through the Kubernetes API |
| `lmdb` | *by default* | Enable using LMDB to store Garage's metadata |
| `metrics` | *by default* | Enable collection of metrics in Prometheus format on the admin API |
| `sqlite` | *by default* | Enable using Sqlite3 to store Garage's metadata |
| `syslog` | optional | Enable logging to Syslog with<br>`GARAGE_LOG_TO_SYSLOG=true` environment variable set |
| `system-libs` | optional | Use system version of sqlite3, zstd, lmdb and libsodium<br>if available (exclusive with `bundled-libs`, build using<br>`cargo build --no-default-features --features system-libs`) |
| `telemetry-otlp` | optional | Enable collection of execution traces using OpenTelemetry |
| `sled` | *by default* | Enable using Sled to store Garage's metadata |
| `lmdb` | optional | Enable using LMDB to store Garage's metadata |
| `sqlite` | optional | Enable using Sqlite3 to store Garage's metadata |
If you want to manage the CustomRessourceDefinition used by garage for its `kubernetes_discovery` outside of the helm chart, add `garage.kubernetesSkipCrd: true` to your custom values and use the kustomization before deploying the helm chart:
After deploying, cluster layout must be configured manually as described in [Creating a cluster layout](@/documentation/quick-start/_index.md#creating-a-cluster-layout). Use the following command to access garage CLI:
```bash
@@ -45,7 +52,7 @@ This is an example `values.overrride.yaml` for deploying in a microk8s cluster w
If your `StorageClass` does not support volume expansion, double check if you can enable it. Otherwise, your only real option is to spin up a new Garage cluster with increased size and migrate all data over.
If your `StorageClass` supports expansion, you are free to continue.
### Increase the size of the PVCs
Increase the size of all PVCs to your desired size.
```bash
kubectl -n garage edit pvc data-garage-0
kubectl -n garage edit pvc data-garage-1
kubectl -n garage edit pvc data-garage-2
kubectl -n garage edit pvc meta-garage-0
kubectl -n garage edit pvc meta-garage-1
kubectl -n garage edit pvc meta-garage-2
```
### Increase the size of the `StatefulSet` PVC template
This is an optional step, but if not done, future instances of Garage will be created with the original size from the template.
This will remove the Garage `StatefulSet` but leave the pods running. It may seem destructive but needs to be done this way since edits to the size of PVC templates are prohibited.
### Redeploy the `StatefulSet`
Now the size of future PVCs can be increased, and the Garage Helm chart can be upgraded. The new `StatefulSet` should take ownership of the orphaned pods again.
This will allow anyone to scrape Prometheus metrics by fetching
`http://localhost:3093/metrics`. If you want to restrict access
`http://localhost:3903/metrics`. If you want to restrict access
to the exported metrics, set the `metrics_token` configuration value
to a bearer token to be used when fetching the metrics endpoint.
@@ -49,9 +49,5 @@ add the following lines in your Prometheus scrape config:
To visualize the scraped data in Grafana,
you can either import our [Grafana dashboard for Garage](https://git.deuxfleurs.fr/Deuxfleurs/garage/raw/branch/main/script/telemetry/grafana-garage-dashboard-prometheus.json)
or make your own.
We detail below the list of exposed metrics and their meaning.
## List of exported metrics
See our [dedicated page](@/documentation/reference-manual/monitoring.md) in the Reference manual section.
The list of exported metrics is available on our [dedicated page](@/documentation/reference-manual/monitoring.md) in the Reference manual section.
@@ -19,14 +19,15 @@ To run a real-world deployment, make sure the following conditions are met:
- You have at least three machines with sufficient storage space available.
- Each machine has a public IP address which is reachable by other machines. It
is highly recommended that you use IPv6 for this end-to-end connectivity. If
IPv6 is not available, then using a mesh VPN such as
- Each machine has an IP address which makes it directly reachable by all other machines.
In many cases, nodes will be behind a NAT and will not each have a public
IPv4 addresses. In this case, is recommended that you use IPv6 for this
end-to-end connectivity if it is available. Otherwise, using a mesh VPN such as
[Nebula](https://github.com/slackhq/nebula) or
[Yggdrasil](https://yggdrasil-network.github.io/) are approaches to consider
in addition to building out your own VPN tunneling.
- This guide will assume you are using Docker containers to deploy Garage on each node.
- This guide will assume you are using Docker containers to deploy Garage on each node.
Garage can also be run independently, for instance as a [Systemd service](@/documentation/cookbook/systemd.md).
You can also use an orchestrator such as Nomad or Kubernetes to automatically manage
Docker containers on a fleet of nodes.
@@ -42,7 +43,7 @@ For our example, we will suppose the following infrastructure with IPv6 connecti
| Brussels | Mars | fc00:F::1 | 1.5 TB |
Note that Garage will **always** store the three copies of your data on nodes at different
locations. This means that in the case of this small example, the available capacity
locations. This means that in the case of this small example, the usable capacity
of the cluster is in fact only 1.5 TB, because nodes in Brussels can't store more than that.
This also means that nodes in Paris and London will be under-utilized.
To make better use of the available hardware, you should ensure that the capacity
@@ -52,9 +53,9 @@ to store 2 TB of data in total.
### Best practices
- If you have fast dedicated networking between all your nodes, and are planing to store
very large files, bump the `block_size` configuration parameter to 10 MB
(`block_size = 10485760`).
- If you have reasonably fast networking between all your nodes, and are planing to store
mostly large files, bump the `block_size` configuration parameter to 10 MB
(`block_size = "10M"`).
- Garage stores its files in two locations: it uses a metadata directory to store frequently-accessed
small metadata items, and a data directory to store data blocks of uploaded objects.
@@ -67,36 +68,42 @@ to store 2 TB of data in total.
EXT4 is not recommended as it has more strict limitations on the number of inodes,
which might cause issues with Garage when large numbers of objects are stored.
-If you only have an HDD and no SSD, it's fine to put your metadata alongside the data
on the same drive. Having lots of RAM for your kernel to cache the metadata will
help a lot with performance. Make sure to use the LMDB database engine,
instead of Sled, which suffers from quite bad performance degradation on HDDs.
Sled is still the default for legacy reasons, but is not recommended anymore.
-Servers with multiple HDDs are supported natively by Garage without resorting
to RAID, see [our dedicated documentation page](@/documentation/operations/multi-hdd.md).
- For the metadata storage, Garage does not do checksumming and integrity
verification on its own. If you are afraid of bitrot/data corruption,
put your metadata directory on a BTRFS partition. Otherwise, just use regular
EXT4 or XFS.
verification on its own, so it is better to use a robust filesystem such as
BTRFS or ZFS. Users have reported that when using the LMDB database engine
(the default), database files have a tendency of becoming corrupted after an
unclean shutdown (e.g. a power outage), so you should take regular snapshots
to be able to recover from such a situation. This can be done using Garage's
built-in automatic snapshotting (since v0.9.4), or by using filesystem level
snapshots. If you cannot do so, you might want to switch to Sqlite which is
more robust.
-Having a single server with several storage drives is currently not very well
supported in Garage ([#218](https://git.deuxfleurs.fr/Deuxfleurs/garage/issues/218)).
For an easy setup, just put all your drives in a RAID0 or a ZFS RAIDZ array.
If you're adventurous, you can try to format each of your disk as
a separate XFS partition, and then run one `garage` daemon per disk drive,
or use something like [`mergerfs`](https://github.com/trapexit/mergerfs) to merge
all your disks in a single union filesystem that spreads load over them.
-LMDB is the fastest and most tested database engine, but it has the following
weaknesses: 1/ data files are not architecture-independent, you cannot simply
move a Garage metadata directory between nodes running different architectures,
and 2/ LMDB is not suited for 32-bit platforms. Sqlite is a viable alternative
if any of these are of concern.
- If you only have an HDD and no SSD, it's fine to put your metadata alongside
the data on the same drive, but then consider your filesystem choice wisely
(see above). Having lots of RAM for your kernel to cache the metadata will
help a lot with performance. The default LMDB database engine is the most
tested and has good performance.
## Get a Docker image
Our docker image is currently named `dxflrs/garage` and is stored on the [Docker Hub](https://hub.docker.com/r/dxflrs/garage/tags?page=1&ordering=last_updated).
We encourage you to use a fixed tag (eg. `v0.8.0`) and not the `latest` tag.
For this example, we will use the latest published version at the time of the writing which is `v0.8.0` but it's up to you
We encourage you to use a fixed tag (eg. `v2.2.0`) and not the `latest` tag.
For this example, we will use the latest published version at the time of the writing which is `v2.2.0` but it's up to you
to check [the most recent versions on the Docker Hub](https://hub.docker.com/r/dxflrs/garage/tags?page=1&ordering=last_updated).
For example:
```
sudo docker pull dxflrs/garage:v0.8.0
sudo docker pull dxflrs/garage:v2.2.0
```
## Deploying and configuring Garage
@@ -119,8 +126,9 @@ A valid `/etc/garage.toml` for our cluster would look as follows:
metadata_dir="/var/lib/garage/meta"
data_dir="/var/lib/garage/data"
db_engine="lmdb"
metadata_auto_snapshot_interval="6h"
replication_mode="3"
replication_factor=3
compression_level=2
@@ -144,6 +152,8 @@ Check the following for your configuration files:
- Make sure `rpc_public_addr` contains the public IP address of the node you are configuring.
This parameter is optional but recommended: if your nodes have trouble communicating with
one another, consider adding it.
Alternatively, you can also set `rpc_public_addr_subnet`, which can filter
the addresses announced to other peers to a specific subnet.
- Make sure `rpc_secret` is the same value on all nodes. It should be a 32-bytes hex-encoded secret key.
You can generate such a key with `openssl rand -hex 32`.
@@ -161,12 +171,13 @@ docker run \
-v /etc/garage.toml:/etc/garage.toml \
-v /var/lib/garage/meta:/var/lib/garage/meta \
-v /var/lib/garage/data:/var/lib/garage/data \
dxflrs/garage:v0.8.0
dxflrs/garage:v2.2.0
```
It should be restarted automatically at each reboot.
Please note that we use host networking as otherwise Docker containers
can not communicate with IPv6.
With this command line, Garage should be started automatically at each boot.
Please note that we use host networking as otherwise the network indirection
added by Docker would prevent Garage nodes from communicating with one another
(especially if using IPv6).
If you want to use `docker-compose`, you may use the following `docker-compose.yml` file as a reference:
@@ -174,7 +185,7 @@ If you want to use `docker-compose`, you may use the following `docker-compose.y
version:"3"
services:
garage:
image:dxflrs/garage:v0.8.0
image:dxflrs/garage:v2.2.0
network_mode:"host"
restart:unless-stopped
volumes:
@@ -183,12 +194,14 @@ services:
- /var/lib/garage/data:/var/lib/garage/data
```
Upgrading between Garage versions should be supported transparently,
but please check the relase notes before doing so!
To upgrade, simply stop and remove this container and
start again the command with a new version of Garage.
If you wish to upgrade your cluster, make sure to read the corresponding
[documentation page](@/documentation/operations/upgrading.md) first, as well as
the documentation relevant to your version of Garage in the case of major
upgrades. With the containerized setup proposed here, the upgrade process
will require stopping and removing the existing container, and re-creating it
with the upgraded version.
## Controling the daemon
## Controlling the daemon
The `garage` binary has two purposes:
- it acts as a daemon when launched with `garage server`
@@ -197,6 +210,12 @@ The `garage` binary has two purposes:
Ensure an appropriate `garage` binary (the same version as your Docker image) is available in your path.
If your configuration file is at `/etc/garage.toml`, the `garage` binary should work with no further change.
You can also use an alias as follows to use the Garage binary inside your docker container:
But at the same time, the `reverse_proxy` is very flexible.
For a production deployment, you should [read its documentation](https://caddyserver.com/docs/caddyfile/directives/reverse_proxy) as it supports features like DNS discovery of upstreams, load balancing with checks, streaming parameters, etc.
### Caching
Caddy can compiled with a
[cache plugin](https://github.com/caddyserver/cache-handler) which can be used
to provide a hot-cache at the webserver-level for static websites hosted by
Garage.
This can be configured as follows:
```caddy
# Caddy global configuration section
{
# Bare minimum configuration to enable cache.
ordercachebeforerewrite
cache
#cache
# allowed_http_verbs GET
# default_cache_control public
# ttl 8h
#}
}
# Site specific section
https://{
cache
#cache {
# timeout {
# backend 30s
# }
#}
reverse_proxy...
}
```
Caching is a complicated subject, and the reader is encouraged to study the
*A note on hardening: garage will be run as a non privileged user, its user id is dynamically allocated by systemd. It cannot access (read or write) home folders (/home, /root and /run/user), the rest of the filesystem can only be read but not written, only the path seen as /var/lib/garage is writable as seen by the service (mapped to /var/lib/private/garage on your host). Additionnaly, the process can not gain new privileges over time.*
**A note on hardening:** Garage will be run as a non privileged user, its user
id is dynamically allocated by systemd (set with `DynamicUser=true`). It cannot
access (read or write) home folders (`/home`, `/root` and `/run/user`), the
rest of the filesystem can only be read but not written, only the path seen as
`/var/lib/garage` is writable as seen by the service. Additionnaly, the process
can not gain new privileges over time.
For this to work correctly, your `garage.toml` must be set with
`metadata_dir=/var/lib/garage/meta` and `data_dir=/var/lib/garage/data`. This
is mandatory to use the DynamicUser hardening feature of systemd, which
autocreates these directories as virtual mapping. If the directory
`/var/lib/garage` already exists before starting the server for the first time,
the systemd service might not start correctly. Note that in your host
filesystem, Garage data will be held in `/var/lib/private/garage`.
To start the service then automatically enable it at boot:
@@ -42,15 +42,30 @@ locations. They use Garage themselves for the following tasks:
- As a [Matrix media backend](https://github.com/matrix-org/synapse-s3-storage-provider)
- To store personal data and shared documents through [Bagage](https://git.deuxfleurs.fr/Deuxfleurs/bagage), a homegrown WebDav-to-S3 proxy
- In the Drone continuous integration platform to store task logs
- As a Nix binary cache
-As a backup target using `rclone`
-To store personal data and shared documents through [Bagage](https://git.deuxfleurs.fr/Deuxfleurs/bagage), a homegrown WebDav-to-S3 and SFTP-to-S3 proxy
- As a backup target using `rclone` and `restic`
The Deuxfleurs Garage cluster is a multi-site cluster currently composed of
4 nodes in 2 physical locations. In the future it will be expanded to at
least 3 physical locations to fully exploit Garage's potential for high
availability.
9 nodes in 3 physical locations.
### Triplebit
[Triplebit](https://www.triplebit.org) is a non-profit hosting provider and
ISP focused on improving access to privacy-related services. They use
Garage themselves for the following tasks:
- Hosting of their homepage, [privacyguides.org](https://www.privacyguides.org/), and various other static sites
- As a PowerDNS authoritative zone backend through [Lightning Stream](https://doc.powerdns.com/lightningstream/latest/index.html) and [LMDB](https://doc.powerdns.com/authoritative/backends/lmdb.html)
- As a Mastodon media storage backend for [mstdn.party](https://mstdn.party/) and [mstdn.plus](https://mstdn.plus/)
- As a PeerTube storage backend for [neat.tube](https://neat.tube/)
- As a [Matrix media backend](https://github.com/matrix-org/synapse-s3-storage-provider)
Triplebit's Garage cluster is a multi-site cluster currently composed of
@@ -67,7 +67,7 @@ Pithos has been abandonned and should probably not used yet, in the following we
Pithos was relying as a S3 proxy in front of Cassandra (and was working with Scylla DB too).
From its designers' mouth, storing data in Cassandra has shown its limitations justifying the project abandonment.
They built a closed-source version 2 that does not store blobs in the database (only metadata) but did not communicate further on it.
We considered there v2's design but concluded that it does not fit both our *Self-contained & lightweight* and *Simple* properties. It makes the development, the deployment and the operations more complicated while reducing the flexibility.
We considered their v2's design but concluded that it does not fit both our *Self-contained & lightweight* and *Simple* properties. It makes the development, the deployment and the operations more complicated while reducing the flexibility.
Garage automatically resyncs all entries stored in the metadata tables every hour,
to ensure that all nodes have the most up-to-date version of all the information
they should be holding.
The resync procedure is based on a Merkle tree that allows to efficiently find
differences between nodes.
In some special cases, e.g. before an upgrade, you might want to run a table
resync manually. This can be done using `garage repair tables`.
## Metadata table reference fixes
In some very rare cases where nodes are unavailable, some references between objects
are broken. For instance, if an object is deleted, the underlying versions or data
blocks may still be held by Garage. If you suspect that such corruption has occurred
in your cluster, you can run one of the following repair procedures:
- `garage repair versions`: checks that all versions belong to a non-deleted object, and purges any orphan version
- `garage repair block-refs`: checks that all block references belong to a non-deleted object version, and purges any orphan block reference (this will then allow the blocks to be garbage-collected)
- `garage repair block-rc`: checks that the reference counters for blocks are in sync with the actual number of non-deleted entries in the block reference table
The cluster layout in Garage is a table that assigns to each node a role in
the cluster. The role of a node in Garage can either be a storage node with
a certain capacity, or a gateway node that does not store data and is only
used as an API entry point for faster cluster access.
An introduction to building cluster layouts can be found in the [production deployment](@/documentation/cookbook/real-world.md) page.
In Garage, all of the data that can be stored in a given cluster is divided
into slices which we call *partitions*. Each partition is stored by
one or several nodes in the cluster
(see [`replication_factor`](@/documentation/reference-manual/configuration.md#replication_factor)).
The layout determines the correspondence between these partitions,
which exist on a logical level, and actual storage nodes.
## How cluster layouts work in Garage
A cluster layout is composed of the following components:
- a table of roles assigned to nodes, defined by the user
- an optimal assignation of partitions to nodes, computed by an algorithm that is ran once when calling `garage layout apply` or the ApplyClusterLayout API endpoint
- a version number
Garage nodes will always use the cluster layout with the highest version number.
Garage nodes also maintain and synchronize between them a set of proposed role
changes that haven't yet been applied. These changes will be applied (or
canceled) in the next version of the layout.
All operations on the layout can be realized using the `garage` CLI or using the
[administration API endpoint](@/documentation/reference-manual/admin-api.md).
We give here a description of CLI commands, the admin API semantics are very similar.
The following commands insert modifications to the set of proposed role changes
for the next layout version (but they do not create the new layout immediately):
```bash
garage layout assign [...]
garage layout remove [...]
```
The following command can be used to inspect the layout that is currently set in the cluster
and the changes proposed for the next layout version, if any:
```bash
garage layout show
```
The following commands create a new layout with the specified version number,
that either takes into account the proposed changes or cancels them:
**WARNING.** At this point, there is no comittement to stability of the APIs described in this document.
We will bump the version numbers prefixed to each API endpoint at each time the syntax
or semantics change, meaning that code that relies on these endpoint will break
when changes are introduced.
The current version of the admin API is v2. No breaking changes to the Garage
administration API will be published outside of a major release.
The Garage administration API was introduced in version 0.7.2, this document
does not apply to older versions of Garage.
History of previous versions:
- Before Garage v0.7.2 - no admin API
- Garage v0.7.2 - admin API v0
- Garage v0.9.0 - admin API v1, deprecate admin API v0
- Garage v2.0.0 - admin API v2, deprecate admin API v1
## Access control
The admin API uses two different tokens for acces control, that are specified in the config file's `[admin]` section:
### Using an API token
- `metrics_token`: the token for accessing the Metrics endpoint (if this token
is not set in the config file, the Metrics endpoint can be accessed without
access control);
- `admin_token`: the token for accessing all of the other administration
endpoints (if this token is not set in the config file, access to these
endpoints is disabled entirely).
These tokens are used as simple HTTP bearer tokens. In other words, to
authenticate access to an admin API endpoint, add the following HTTP header
to your request:
Administration API tokens tokens are used as simple HTTP bearer tokens. In
other words, to authenticate access to an admin API endpoint, add the following
HTTP header to your request:
```
Authorization: Bearer <token>
```
## Administration API endpoints
### User-defined API tokens
### Metrics-related endpoints
Cluster administrators may dynamically define administration tokens using the CLI commands under `garage admin-token`.
Such tokens may be limited in scope, meaning that they may enable access to only a subset of API calls.
They may also have an expiration date to limit their use in time.
#### Metrics `GET /metrics`
Returns internal Garage metrics in Prometheus format.
### Cluster operations
These endpoints are defined on a dedicated [Redocly page](https://garagehq.deuxfleurs.fr/api/garage-admin-v0.html). You can also download its [OpenAPI specification](https://garagehq.deuxfleurs.fr/api/garage-admin-v0.yml).
Requesting the API from the command line can be as simple as running:
Here is an example to create an administration token that is valid for 30 days
and gives access to only a subset of API calls, allowing it to create buckets
and access keys and give keys permissions on buckets:
# HELP api_admin_request_duration Duration of API calls to the various Admin API endpoints
...
```
### Health `GET /health`
Returns `200 OK` if enough nodes are up to have a quorum (ie. serve requests),
otherwise returns `503 Service Unavailable`.
**Example:**
```
$ curl -i http://localhost:3903/health
HTTP/1.1 200 OK
content-type: text/plain
content-length: 102
date: Tue, 08 Aug 2023 07:22:38 GMT
Garage is fully operational
Consult the full health check API endpoint at /v2/GetClusterHealth for more details
```
### On-demand TLS `GET /check`
To prevent abuse for on-demand TLS, Caddy developers have specified an endpoint that can be queried by the reverse proxy
to know if a given domain is allowed to get a certificate. Garage implements these endpoints to tell if a given domain is handled by Garage or is garbage.
Garage responds with the following logic:
- If the domain matches the pattern `<bucket-name>.<s3_api.root_domain>`, returns 200 OK
- If the domain matches the pattern `<bucket-name>.<s3_web.root_domain>` and website is configured for `<bucket>`, returns 200 OK
- If the domain matches the pattern `<bucket-name>` and website is configured for `<bucket>`, returns 200 OK
- Otherwise, returns 404 Not Found, 400 Bad Request or 5xx requests.
*Note 1: because in the path-style URL mode, there is only one domain that is not known by Garage, hence it is not supported by this API endpoint.
You must manually declare the domain in your reverse-proxy. Idem for K2V.*
*Note 2: buckets in a user's namespace are not supported yet by this endpoint. This is a limitation of this endpoint currently.*
**Example:** Suppose a Garage instance is configured with `s3_api.root_domain = .s3.garage.localhost` and `s3_web.root_domain = .web.garage.localhost`.
With a private `media` bucket (name in the global namespace, website is disabled), the endpoint will feature the following behavior:
- [Add option for a backend check to approve use of on-demand TLS](https://github.com/caddyserver/caddy/pull/1939)
- [Serving tens of thousands of domains over HTTPS with Caddy](https://caddy.community/t/serving-tens-of-thousands-of-domains-over-https-with-caddy/11179)
and the hashes of individual blocks are used to dispatch them to storage nodes
and to deduplicate them.
### No RAFT slowing you down
@@ -46,14 +61,7 @@ directed to a Garage cluster can be handled independently of one another instead
of going through a central bottleneck (the leader node).
As a consequence, requests can be handled much faster, even in cases where latency
between cluster nodes is important (see our [benchmarks](@/documentation/design/benchmarks/index.md) for data on this).
This is particularly usefull when nodes are far from one another and talk to one other through standard Internet connections.
### Several replication modes
Garage supports a variety of replication modes, with 1 copy, 2 copies or 3 copies of your data,
and with various levels of consistency, in order to adapt to a variety of usage scenarios.
Read our reference page on [supported replication modes](@/documentation/reference-manual/configuration.md#replication-mode)
to select the replication mode best suited to your use case (hint: in most cases, `replication_mode = "3"` is what you want).
This is particularly useful when nodes are far from one another and talk to one other through standard Internet connections.
### Web server for static websites
@@ -121,5 +129,5 @@ related to objects stored in an S3 bucket.
In the context of our research project, [Aérogramme](https://aerogramme.deuxfleurs.fr),
K2V is used to provide metadata and log storage for operations on encrypted e-mail storage.
Learn more on the specification of K2V [here](https://git.deuxfleurs.fr/Deuxfleurs/garage/src/branch/k2v/doc/drafts/k2v-spec.md)
Learn more on the specification of K2V [here](https://git.deuxfleurs.fr/Deuxfleurs/garage/src/commit/f8be15c37db857e177d543de7be863692628d567/doc/drafts/k2v-spec.md)
and on how to enable it in Garage [here](@/documentation/reference-manual/k2v.md).
@@ -42,7 +42,7 @@ The general principle are similar, but details have not been updated.**
A version is defined by the existence of at least one entry in the blocks table for a certain version UUID.
We must keep the following invariant: if a version exists in the blocks table, it has to be referenced in the objects table.
We explicitly manage concurrent versions of an object: the version timestamp and version UUID columns are index columns, thus we may have several concurrent versions of an object.
Important: before deleting an older version from the objects table, we must make sure that we did a successfull delete of the blocks of that version from the blocks table.
Important: before deleting an older version from the objects table, we must make sure that we did a successful delete of the blocks of that version from the blocks table.
Thus, the workflow for reading an object is as follows:
@@ -95,7 +95,7 @@ Known issue: if someone is reading from a version that we want to delete and the
Usefull metadata:
- list of versions that reference this block in the Casandra table, so that we can do GC by checking in Cassandra that the lines still exist
- list of other nodes that we know have acknowledged a write of this block, usefull in the rebalancing algorithm
- list of other nodes that we know have acknowledged a write of this block, useful in the rebalancing algorithm
Write strategy: have a single thread that does all write IO so that it is serialized (or have several threads that manage independent parts of the hash space). When writing a blob, write it to a temporary file, close, then rename so that a concurrent read gets a consistent result (either not found or found with whole content).
**This guide explains how to migrate to 0.9 if you have an existing 0.8 cluster.
We don't recommend trying to migrate to 0.9 directly from 0.7 or older.**
This migration procedure has been tested on several clusters without issues.
However, it is still a *critical procedure* that might cause issues.
**Make sure to back up all your data before attempting it!**
You might also want to read our [general documentation on upgrading Garage](@/documentation/operations/upgrading.md).
The following are **breaking changes** in Garage v0.9 that require your attention when migrating:
- LMDB is now the default metadata db engine and Sled is deprecated. If you were using Sled, make sure to specify `db_engine = "sled"` in your configuration file, or take the time to [convert your database](https://garagehq.deuxfleurs.fr/documentation/reference-manual/configuration/#db-engine-since-v0-8-0).
- Capacity values are now in actual byte units. The translation from the old layout will assign 1 capacity = 1Gb by default, which might be wrong for your cluster. This does not cause any data to be moved around, but you might want to re-assign correct capacity values post-migration.
- Multipart uploads that were started in Garage v0.8 will not be visible in Garage v0.9 and will have to be restarted from scratch.
- Changes to the admin API: some `v0/` endpoints have been replaced by `v1/` counterparts with updated/uniformized syntax. All other endpoints have also moved to `v1/` by default, without syntax changes, but are still available under `v0/` for compatibility.
## Simple migration procedure (takes cluster offline for a while)
The migration steps are as follows:
1. Disable API and web access. You may do this by stopping your reverse proxy or by commenting out
the `api_bind_addr` values in your `config.toml` file and restarting Garage.
2. Do `garage repair --all-nodes --yes tables` and `garage repair --all-nodes --yes blocks`,
check the logs and check that all data seems to be synced correctly between
nodes. If you have time, do additional checks (`versions`, `block_refs`, etc.)
3. Check that the block resync queue and Merkle queue are empty:
run `garage stats -a` to query them or inspect metrics in the Grafana dashboard.
4. Turn off Garage v0.8
5. **Backup the metadata folder of all your nodes!** For instance, use the following command
if your metadata directory is `/var/lib/garage/meta`: `cd /var/lib/garage ; tar -acf meta-v0.8.tar.zst meta/`
6. Install Garage v0.9
7. Update your configuration file if necessary.
8. Turn on Garage v0.9
9. Do `garage repair --all-nodes --yes tables` and `garage repair --all-nodes --yes blocks`.
Wait for a full table sync to run.
10. Your upgraded cluster should be in a working state. Re-enable API and Web
access and check that everything went well.
11. Monitor your cluster in the next hours to see if it works well under your production load, report any issue.
12. You might want to assign correct capacity values to all your nodes. Doing so might cause data to be moved
in your cluster, which should also be monitored carefully.
## Minimal downtime migration procedure
The migration to Garage v0.9 can be done with almost no downtime,
by restarting all nodes at once in the new version.
The migration steps are as follows:
1. Do `garage repair --all-nodes --yes tables` and `garage repair --all-nodes --yes blocks`,
check the logs and check that all data seems to be synced correctly between
nodes. If you have time, do additional checks (`versions`, `block_refs`, etc.)
2. Turn off each node individually; back up its metadata folder (see above); turn it back on again.
This will allow you to take a backup of all nodes without impacting global cluster availability.
You can do all nodes of a single zone at once as this does not impact the availability of Garage.
3. Prepare your binaries and configuration files for Garage v0.9
4. Shut down all v0.8 nodes simultaneously, and restart them all simultaneously in v0.9.
Use your favorite deployment tool (Ansible, Kubernetes, Nomad) to achieve this as fast as possible.
Garage v0.9 should be in a working state as soon as it starts.
5. Proceed with repair and monitoring as described in steps 9-12 above.
Garage\footnote{\url{https://garagehq.deuxfleurs.fr/}} is an open-source distributed object storage service tailored for self-hosting. It was designed by the Deuxfleurs association\footnote{\url{https://deuxfleurs.fr/}} to enable small structures (associations, collectives, small companies) to share storage resources to reliably self-host their data, possibly with old and non-reliable machines.
To achieve these reliability and availability goals, the data is broken into \emph{partitions} and every partition is replicated over 3 different machines (that we call \emph{nodes}). When the data is queried, a consensus algorithm allows to fetch it from one of the nodes. A \emph{replication factor} of 3 ensures the best guarantees in the consensus algorithm \cite{ADD RREF}, but this parameter can be different.
Moreover, if the nodes are spread over different \emph{zones} (different houses, offices, cities\dots), we can ask the data to be replicated over nodes belonging to different zones, to improve the storage robustness against zone failure (such as power outage). To do so, we set a \emph{redundancy parameter}, that is no more than the replication factor, and we ask that any partition is replicated over this number of zones at least.
In this work, we propose a repartition algorithm that, given the nodes specifications and the replication and redundancy parameters, computes an optimal assignation of partitions to nodes. We say that the assignation is optimal in the sense that it maximizes the size of the partitions, and hence the effective storage capacity of the system.
Moreover, when a former assignation exists, which is not optimal anymore due to nodes or zones updates, our algorithm computes a new optimal assignation that minimizes the amount of data to be transferred during the assignation update (the \emph{transfer load}).
We call the set of nodes cooperating to store the data a \emph{cluster}, and a description of the nodes, zones and the assignation of partitions to nodes a \emph{cluster layout}
\subsection{Notations}
Let $k$ be some fixed parameter value, typically 8, that we call the ``partition bits''.
Every object to be stored in the system is split into data blocks of fixed size. We compute a hash $h(\mathbf{b})$ of every such block $\mathbf{b}$, and we define the $k$ last bits of this hash to be the partition number $p(\mathbf{b})$ of the block. This label can take $P=2^k$ different values, and hence there are $P$ different partitions. We denote $\mathbf{P}$ the set of partition labels (i.e. $\mathbf{P}=\llbracket1,P\rrbracket$).
We are given a set $\mathbf{N}$ of $N$ nodes and a set $\mathbf{Z}$ of $Z$ zones. Every node $n$ has a non-negative storage capacity $c_n\ge0$ and belongs to a zone $z_n\in\mathbf{Z}$. We are also given a replication parameter $\rho_\mathbf{N}$ and a redundancy parameter $\rho_\mathbf{Z}$ such that $1\le\rho_\mathbf{Z}\le\rho_\mathbf{N}$ (typical values would be $\rho_N=3$ and $\rho_Z=2$).
Our goal is to compute an assignment $\alpha=(\alpha_p^1, \ldots, \alpha_p^{\rho_\mathbf{N}})_{p\in\mathbf{P}}$ such that every partition $p$ is associated to $\rho_\mathbf{N}$ distinct nodes $\alpha_p^1, \ldots, \alpha_p^{\rho_\mathbf{N}}\in\mathbf{N}$ and these nodes belong to at least $\rho_\mathbf{Z}$ distinct zones. Among the possible assignations, we choose one that \emph{maximizes} the effective storage capacity of the cluster. If the layout contained a previous assignment $\alpha'$, we \emph{minimize} the amount of data to transfer during the layout update by making $\alpha$ as close as possible to $\alpha'$. These maximization and minimization are described more formally in the following section.
\subsection{Optimization parameters}
To link the effective storage capacity of the cluster to partition assignment, we make the following assumption:
\begin{equation}
\tag{H1}
\text{\emph{All partitions have the same size $s$.}}
\end{equation}
This assumption is justified by the dispersion of the hashing function, when the number of partitions is small relative to the number of stored blocks.
Every node $n$ wille store some number $p_n$ of partitions (it is the number of partitions $p$ such that $n$ appears in the $\alpha_p$). Hence the partitions stored by $n$ (and hence all partitions by our assumption) have there size bounded by $c_n/p_n$. This remark leads us to define the optimal size that we will want to maximize:
\begin{equation}
\label{eq:optimal}
\tag{OPT}
s^* = \min_{n \in N}\frac{c_n}{p_n}.
\end{equation}
When the capacities of the nodes are updated (this includes adding or removing a node), we want to update the assignment as well. However, transferring the data between nodes has a cost and we would like to limit the number of changes in the assignment. We make the following assumption:
\begin{equation}
\tag{H2}
\text{\emph{Nodes updates happen rarely relatively to block operations.}}
\end{equation}
This assumption justifies that when we compute the new assignment $\alpha$, it is worth to optimize the partition size \eqref{eq:optimal} first, and then, among the possible optimal solution, to try to minimize the number of partition transfers. More formally, we minimize the distance between two assignments defined by
where the symmetric difference $\alpha_p \triangle\alpha'_p$ denotes the nodes appearing in one of the assignations but not in both.
\section{Computation of an optimal assignment}
The algorithm that we propose takes as inputs the cluster layout parameters $\mathbf{N}$, $\mathbf{Z}$, $\mathbf{P}$, $(c_n)_{n\in\mathbf{N}}$, $\rho_\mathbf{N}$, $\rho_\mathbf{Z}$, that we defined in the introduction, together with the former assignation $\alpha'$ (if any). The computation of the new optimal assignation $\alpha^*$ is done in three successive steps that will be detailed in the following sections. The first step computes the largest partition size $s^*$ that an assignation can achieve. The second step computes an optimal candidate assignment $\alpha$ that achieves $s^*$ and a heuristic is used in the computation to make it hopefully close to $\alpha'$. The third steps modifies $\alpha$ iteratively to reduces $d(\alpha, \alpha')$ and yields an assignation $\alpha^*$ achieving $s^*$, and minimizing $d(\cdot, \alpha')$ among such assignations.
We will explain in the next section how to represent an assignment $\alpha$ by a flow $f$ on a weighted graph $G$ to enable the use of flow and graph algorithms. The main function of the algorithm can be written as follows.
\State$f^*\leftarrow$\Call{Minimize transfer load}{$G$, $f$, $\alpha'$}
\State Build $\alpha^*$ from $f^*$
\State\Return$\alpha^*$
\EndFunction
\end{algorithmic}
\subsubsection*{Complexity}
As we will see in the next sections, the worst case complexity of this algorithm is $O(P^2 N^2)$. The minimization of transfer load is the most expensive step, and it can run with a timeout since it is only an optimization step. Without this step (or with a smart timeout), the worst cas complexity can be $O((PN)^{3/2}\log C)$ where $C$ is the total storage capacity of the cluster.
\subsection{Determination of the partition size $s^*$}
We will represent an assignment $\alpha$ as a flow in a specific graph $G$. We will not compute the optimal partition size $s^*$ a priori, but we will determine it by dichotomy, as the largest size $s$ such that the maximal flow achievable on $G=G(s)$ has value $\rho_\mathbf{N}P$. We will assume that the capacities are given in a small enough unit (say, Megabytes), and we will determine $s^*$ at the precision of the given unit.
Given some candidate size value $s$, we describe the oriented weighted graph $G=(V,E)$ with vertex set $V$ arc set $E$ (see Figure \ref{fig:flowgraph}).
The set of vertices $V$ contains the source $\mathbf{s}$, the sink $\mathbf{t}$, vertices
$\mathbf{p^+, p^-}$ for every partition $p$, vertices $\mathbf{x}_{p,z}$ for every partition $p$ and zone $z$, and vertices $\mathbf{n}$ for every node $n$.
The set of arcs $E$ contains:
\begin{itemize}
\item ($\mathbf{s}$,$\mathbf{p}^+$, $\rho_\mathbf{Z}$) for every partition $p$;
\item ($\mathbf{s}$,$\mathbf{p}^-$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$;
\item ($\mathbf{p}^+$,$\mathbf{x}_{p,z}$, 1) for every partition $p$ and zone $z$;
\item ($\mathbf{p}^-$,$\mathbf{x}_{p,z}$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$ and zone $z$;
\item ($\mathbf{x}_{p,z}$,$\mathbf{n}$, 1) for every partition $p$, zone $z$ and node $n\in z$;
\item ($\mathbf{n}$, $\mathbf{t}$, $\lfloor c_n/s \rfloor$) for every node $n$.
\caption{An example of graph $G(s)$. Arcs are oriented from left to right, and unlabeled arcs have capacity 1. In this example, nodes $n_1,n_2,n_3$ belong to zone $z_1$, and nodes $n_4,n_5$ belong to zone $z_2$.}
\label{fig:flowgraph}
\end{figure}
In the following complexity calculations, we will use the number of vertices and edges of $G$. Remark from now that $\# V = O(PZ)$ and $\# E = O(PN)$.
\begin{proposition}
An assignment $\alpha$ is realizable with partition size $s$ and the redundancy constraints $(\rho_\mathbf{N},\rho_\mathbf{Z})$ if and only if there exists a maximal flow function $f$ in $G$ with total flow $\rho_\mathbf{N}P$, such that the arcs ($\mathbf{x}_{p,z}$,$\mathbf{n}$, 1) used are exactly those for which $p$ is associated to $n$ in $\alpha$.
\end{proposition}
\begin{proof}
Given such flow $f$, we can reconstruct a candidate $\alpha$. In $f$, the flow passing through $\mathbf{p^+}$ and $\mathbf{p^-}$ is $\rho_\mathbf{N}$, and since the outgoing capacity of every $\mathbf{x}_{p,z}$ is 1, every partition is associated to $\rho_\mathbf{N}$ distinct nodes. The fraction $\rho_\mathbf{Z}$ of the flow passing through every $\mathbf{p^+}$ must be spread over as many distinct zones as every arc outgoing from $\mathbf{p^+}$ has capacity 1. So the reconstructed $\alpha$ verifies the redundancy constraints. For every node $n$, the flow between $\mathbf{n}$ and $\mathbf{t}$ corresponds to the number of partitions associated to $n$. By construction of $f$, this does not exceed $\lfloor c_n/s \rfloor$. We assumed that the partition size is $s$, hence this association does not exceed the storage capacity of the nodes.
In the other direction, given an assignment $\alpha$, one can similarly check that the facts that $\alpha$ respects the redundancy constraints, and the storage capacities of the nodes, are necessary condition to construct a maximal flow function $f$.
\end{proof}
\textbf{Implementation remark:} In the flow algorithm, while exploring the graph, we explore the neighbours of every vertex in a random order to heuristically spread the associations between nodes and partitions.
\subsubsection*{Algorithm}
With this result mind, we can describe the first step of our algorithm. All divisions are supposed to be integer divisions.
To compute the maximal flow, we use Dinic's algorithm. Its complexity on general graphs is $O(\#V^2\#E)$, but on graphs with edge capacity bounded by a constant, it turns out to be $O(\#E^{3/2})$. The graph $G$ does not fall in this case since the capacities of the arcs incoming to $\mathbf{t}$ are far from bounded. However, the proof of this complexity function works readily for graphs where we only ask the edges \emph{not} incoming to the sink $\mathbf{t}$ to have their capacities bounded by a constant. One can find the proof of this claim in \cite[Section 2]{even1975network}.
The dichotomy adds a logarithmic factor $\log(C)$ where $C=\sum_{n \in\mathbf{N}} c_n$ is the total capacity of the cluster. The total complexity of this first function is hence
$O(\#E^{3/2}\log C )= O\big((PN)^{3/2}\log C\big)$.
\subsubsection*{Metrics}
We can display the discrepancy between the computed $s^*$ and the best size we could have hoped for the given total capacity, that is $C/\rho_\mathbf{N}$.
\subsection{Computation of a candidate assignment}
Now that we have the optimal partition size $s^*$, to compute a candidate assignment it would be enough to compute a maximal flow function $f$ on $G(s^*)$. This is what we do if there is no former assignation $\alpha'$.
If there is some $\alpha'$, we add a step that will heuristically help to obtain a candidate $\alpha$ closer to $\alpha'$. We fist compute a flow function $\tilde{f}$ that uses only the partition-to-node associations appearing in $\alpha'$. Most likely, $\tilde{f}$ will not be a maximal flow of $G(s^*)$. In Dinic's algorithm, we can start from a non maximal flow function and then discover improving paths. This is what we do by starting from $\tilde{f}$. The hope\footnote{This is only a hope, because one can find examples where the construction of $f$ from $\tilde{f}$ produces an assignment $\alpha$ that is not as close as possible to $\alpha'$.} is that the final flow function $f$ will tend to keep the associations appearing in $\tilde{f}$.
More formally, we construct the graph $G_{|\alpha'}$ from $G$ by removing all the arcs $(\mathbf{x}_{p,z},\mathbf{n}, 1)$ where $p$ is not associated to $n$ in $\alpha'$. We compute a maximal flow function $\tilde{f}$ in $G_{|\alpha'}$. The flow $\tilde{f}$ is also a valid (most likely non maximal) flow function on $G$. We compute a maximal flow function $f$ on $G$ by starting Dinic's algorithm on $\tilde{f}$.
\State$ f \leftarrow$\Call{Maximal flow from flow}{$G$, $\tilde{f}$}
\State\Return$f$
\EndFunction
\end{algorithmic}
~
\textbf{Remark:} The function ``Maximal flow'' can be just seen as the function ``Maximal flow from flow'' called with the zero flow function as starting flow.
\subsubsection*{Complexity}
With the considerations of the last section, we have the complexity of the Dinic's algorithm $O(\#E^{3/2})= O((PN)^{3/2})$.
\subsubsection*{Metrics}
We can display the flow value of $\tilde{f}$, which is an upper bound of the distance between $\alpha$ and $\alpha'$. It might be more a Debug level display than Info.
\subsection{Minimization of the transfer load}
Now that we have a candidate flow function $f$, we want to modify it to make its corresponding assignation $\alpha$ as close as possible to $\alpha'$. Denote by $f'$ the maximal flow corresponding to $\alpha'$, and let $d(f, \alpha')=d(f, f'):=d(\alpha,\alpha')$\footnote{It is the number of arcs of type $(\mathbf{x}_{p,z},\mathbf{n})$ saturated in one flow and not in the other.}.
We want to build a sequence $f=f_0, f_1, f_2\dots$ of maximal flows such that $d(f_i, \alpha')$ decreases as $i$ increases. The distance being a non-negative integer, this sequence of flow functions must be finite. We now explain how to find some improving $f_{i+1}$ from $f_i$.
For any maximal flow $f$ in $G$, we define the oriented weighted graph $G_f=(V, E_f)$ as follows. The vertices of $G_f$ are the same as the vertices of $G$. $E_f$ contains the arc $(v_1,v_2, w)$ between vertices $v_1,v_2\in V$ with weight $w$ if and only if the arc $(v_1,v_2)$ is not saturated in $f$ (i.e. $c(v_1,v_2)-f(v_1,v_2)\ge1$, we also consider reversed arcs). The weight $w$ is:
\begin{itemize}
\item$-1$ if $(v_1,v_2)$ is of type $(\mathbf{x}_{p,z},\mathbf{n})$ or $(\mathbf{x}_{p,z},\mathbf{n})$ and is saturated in only one of the two flows $f,f'$;
\item$+1$ if $(v_1,v_2)$ is of type $(\mathbf{x}_{p,z},\mathbf{n})$ or $(\mathbf{x}_{p,z},\mathbf{n})$ and is saturated in either both or none of the two flows $f,f'$;
\item$0$ otherwise.
\end{itemize}
If $\gamma$ is a simple cycle of arcs in $G_f$, we define its weight $w(\gamma)$ as the sum of the weights of its arcs. We can add $+1$ to the value of $f$ on the arcs of $\gamma$, and by construction of $G_f$ and the fact that $\gamma$ is a cycle, the function that we get is still a valid flow function on $G$, it is maximal as it has the same flow value as $f$. We denote this new function $f+\gamma$.
\begin{proposition}
Given a maximal flow $f$ and a simple cycle $\gamma$ in $G_f$, we have $d(f+\gamma, f')- d(f,f')= w(\gamma)$.
\end{proposition}
\begin{proof}
Let $X$ be the set of arcs of type $(\mathbf{x}_{p,z},\mathbf{n})$. Then we can express $d(f,f')$ as
Remark that since we passed on unit of flow in $\gamma$ to construct $f+\gamma$, we have for any $e\in X$, $f(e)=f'(e)$ if and only if $(f+\gamma)(e)\neq f'(e)$.
Plugging this in the previous equation, we find that
$$d(f,f')+w(\gamma)= d(f+\gamma, f').$$
\end{proof}
This result suggests that given some flow $f_i$, we just need to find a negative cycle $\gamma$ in $G_{f_i}$ to construct $f_{i+1}$ as $f_i+\gamma$. The following proposition ensures that this greedy strategy reaches an optimal flow.
\begin{proposition}
For any maximal flow $f$, $G_f$ contains a negative cycle if and only if there exists a maximal flow $f^*$ in $G$ such that $d(f^*, f') < d(f, f')$.
\end{proposition}
\begin{proof}
Suppose that there is such flow $f^*$. Define the oriented multigraph $M_{f,f^*}=(V,E_M)$ with the same vertex set $V$ as in $G$, and for every $v_1,v_2\in V$, $E_M$ contains $(f^*(v_1,v_2)- f(v_1,v_2))_+$ copies of the arc $(v_1,v_2)$. For every vertex $v$, its total degree (meaning its outer degree minus its inner degree) is equal to
The last two sums are zero for any inner vertex since $f,f^*$ are flows, and they are equal on the source and sink since the two flows are both maximal and have hence the same value. Thus, $\deg v =0$ for every vertex $v$.
This implies that the multigraph $M_{f,f^*}$ is the union of disjoint simple cycles. $f$ can be transformed into $f^*$ by pushing a mass 1 along all these cycles in any order. Since $d(f^*, f')<d(f,f')$, there must exists one of these simple cycles $\gamma$ with $d(f+\gamma, f') < d(f, f')$. Finally, since we can push a mass in $f$ along $\gamma$, it must appear in $G_f$. Hence $\gamma$ is a cycle of $G_f$ with negative weight.
\end{proof}
In the next section we describe the corresponding algorithm. Instead of discovering only one cycle, we are allowed to discover a set $\Gamma$ of disjoint negative cycles.
\subsubsection*{Algorithm}
\begin{algorithmic}[1]
\Function{Minimize transfer load}{$G$, $f$, $\alpha'$}
The distance $d(f,f')$ is bounded by the maximal number of differences in the associated assignment. If these assignment are totally disjoint, this distance is $2\rho_N P$. At every iteration of the While loop, the distance decreases, so there is at most $O(\rho_N P)= O(P)$ iterations.
The detection of negative cycle is done with the Bellman-Ford algorithm, whose complexity should normally be $O(\#E\#V)$. In our case, it amounts to $O(P^2ZN)$. Multiplied by the complexity of the outer loop, it amounts to $O(P^3ZN)$ which is a lot when the number of partitions and nodes starts to be large. To avoid that, we adapt the Bellman-Ford algorithm.
The Bellman-Ford algorithm runs $\#V$ iterations of an outer loop, and an inner loop over $E$. The idea is to compute the shortest paths from a source vertex $v$ to all other vertices. After $k$ iterations of the outer loop, the algorithm has computed all shortest path of length at most $k$. All simple paths have length at most $\#V-1$, so if there is an update in the last iteration of the loop, it means that there is a negative cycle in the graph. The observation that will enable us to improve the complexity is the following:
\begin{proposition}
In the graph $G_f$ (and $G$), all simple paths have a length at most $4N$.
\end{proposition}
\begin{proof}
Since $f$ is a maximal flow, there is no outgoing edge from $\mathbf{s}$ in $G_f$. One can thus check than any simple path of length 4 must contain at least two node of type $\mathbf{n}$. Hence on a path, at most 4 arcs separate two successive nodes of type $\mathbf{n}$.
\end{proof}
Thus, in the absence of negative cycles, shortest paths in $G_f$ have length at most $4N$. So we can do only $4N+1$ iterations of the outer loop in the Bellman-Ford algorithm. This makes the complexity of the detection of one set of cycle to be $O(N\#E)= O(N^2 P)$.
With this improvement, the complexity of the whole algorithm is, in the worst case, $O(N^2P^2)$. However, since we detect several cycles at once and we start with a flow that might be close to the previous one, the number of iterations of the outer loop might be smaller in practice.
\subsubsection*{Metrics}
We can display the node and zone utilization ratio, by dividing the flow passing through them divided by their outgoing capacity. In particular, we can pinpoint saturated nodes and zones (i.e. used at their full potential).
We can display the distance to the previous assignment, and the number of partition transfers.
Garage is an open-source distributed storage service blablabla$\dots$
Every object to be stored in the system falls in a partition given by the last $k$ bits of its hash. There are $P=2^k$ partitions. Every partition will be stored on distinct nodes of the system. The goal of the assignment of partitions to nodes is to ensure (nodes and zone) redundancy and to be as efficient as possible.
\subsection{Formal description of the problem}
We are given a set of nodes $\mathbf{N}$ and a set of zones $\mathbf{Z}$. Every node $n$ has a non-negative storage capacity $c_n\ge0$ and belongs to a zone $z\in\mathbf{Z}$. We are also given a number of partition $P>0$ (typically $P=256$).
We would like to compute an assignment of nodes to partitions. We will impose some redundancy constraints to this assignment, and under these constraints, we want our system to have the largest storage capacity possible. To link storage capacity to partition assignment, we make the following assumption:
\begin{equation}
\tag{H1}
\text{\emph{All partitions have the same size $s$.}}
\end{equation}
This assumption is justified by the dispersion of the hashing function, when the number of partitions is small relative to the number of stored large objects.
Every node $n$ wille store some number $k_n$ of partitions. Hence the partitions stored by $n$ (and hence all partitions by our assumption) have there size bounded by $c_n/k_n$. This remark leads us to define the optimal size that we will want to maximize:
\begin{equation}
\label{eq:optimal}
\tag{OPT}
s^* = \min_{n \in N}\frac{c_n}{k_n}.
\end{equation}
When the capacities of the nodes are updated (this includes adding or removing a node), we want to update the assignment as well. However, transferring the data between nodes has a cost and we would like to limit the number of changes in the assignment. We make the following assumption:
\begin{equation}
\tag{H2}
\text{\emph{Updates of capacity happens rarely relatively to object storing.}}
\end{equation}
This assumption justifies that when we compute the new assignment, it is worth to optimize the partition size \eqref{eq:optimal} first, and then, among the possible optimal solution, to try to minimize the number of partition transfers.
For now, in the following, we ask the following redundancy constraint:
\textbf{Parametric node and zone redundancy:} Given two integer parameters $1\le\rho_\mathbf{Z}\le\rho_\mathbf{N}$, we ask every partition to be stored on $\rho_\mathbf{N}$ distinct nodes, and these nodes must belong to at least $\rho_\mathbf{Z}$ distinct zones.
\textbf{Mode 3-strict:} every partition needs to be assignated to three nodes belonging to three different zones.
\textbf{Mode 3:} every partition needs to be assignated to three nodes. We try to spread the three nodes over different zones as much as possible.
\textbf{Warning:} This is a working document written incrementaly. The last version of the algorithm is the \textbf{parametric assignment} described in the next section.
\section{Computation of a parametric assignment}
\textbf{Attention : }We change notations in this section.
Notations : let $P$ be the number of partitions, $N$ the number of nodes, $Z$ the number of zones. Let $\mathbf{P,N,Z}$ be the label sets of, respectively, partitions, nodes and zones.
Let $s^*$ be the largest partition size achievable with the redundancy constraints. Let $(c_n)_{n\in\mathbf{N}}$ be the storage capacity of every node.
In this section, we propose a third specification of the problem. The user inputs two redundancy parameters $1\le\rho_\mathbf{Z}\le\rho_\mathbf{N}$. We compute an assignment $\alpha=(\alpha_p^1, \ldots, \alpha_p^{\rho_\mathbf{N}})_{p\in\mathbf{P}}$ such that every partition $p$ is associated to $\rho_\mathbf{N}$ distinct nodes $\alpha_p^1, \ldots, \alpha_p^{\rho_\mathbf{N}}$ and these nodes belong to at least $\rho_\mathbf{Z}$ distinct zones.
If the layout contained a previous assignment $\alpha'$, we try to minimize the amount of data to transfer during the layout update by making $\alpha$ as close as possible to $\alpha'$.
In the following subsections, we describe the successive steps of the algorithm we propose to compute $\alpha$.
\State$f^*\leftarrow$\Call{Minimize transfer load}{$G$, $f$, $\alpha'$}
\State Build $\alpha^*$ from $f^*$
\State\Return$\alpha^*$
\EndFunction
\end{algorithmic}
\subsubsection*{Complexity}
As we will see in the next sections, the worst case complexity of this algorithm is $O(P^2 N^2)$. The minimization of transfer load is the most expensive step, and it can run with a timeout since it is only an optimization step. Without this step (or with a smart timeout), the worst cas complexity can be $O((PN)^{3/2}\log C)$ where $C$ is the total storage capacity of the cluster.
\subsection{Determination of the partition size $s^*$}
Again, we will represent an assignment $\alpha$ as a flow in a specific graph $G$. We will not compute the optimal partition size $s^*$ a priori, but we will determine it by dichotomy, as the largest size $s$ such that the maximal flow achievable on $G=G(s)$ has value $\rho_\mathbf{N}P$. We will assume that the capacities are given in a small enough unit (say, Megabytes), and we will determine $s^*$ at the precision of the given unit.
Given some candidate size value $s$, we describe the oriented weighted graph $G=(V,E)$ with vertex set $V$ arc set $E$.
The set of vertices $V$ contains the source $\mathbf{s}$, the sink $\mathbf{t}$, vertices
$\mathbf{p^+, p^-}$ for every partition $p$, vertices $\mathbf{x}_{p,z}$ for every partition $p$ and zone $z$, and vertices $\mathbf{n}$ for every node $n$.
The set of arcs $E$ contains:
\begin{itemize}
\item ($\mathbf{s}$,$\mathbf{p}^+$, $\rho_\mathbf{Z}$) for every partition $p$;
\item ($\mathbf{s}$,$\mathbf{p}^-$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$;
\item ($\mathbf{p}^+$,$\mathbf{x}_{p,z}$, 1) for every partition $p$ and zone $z$;
\item ($\mathbf{p}^-$,$\mathbf{x}_{p,z}$, $\rho_\mathbf{N}-\rho_\mathbf{Z}$) for every partition $p$ and zone $z$;
\item ($\mathbf{x}_{p,z}$,$\mathbf{n}$, 1) for every partition $p$, zone $z$ and node $n\in z$;
\item ($\mathbf{n}$, $\mathbf{t}$, $\lfloor c_n/s \rfloor$) for every node $n$.
\end{itemize}
In the following complexity calculations, we will use the number of vertices and edges of $G$. Remark from now that $\# V = O(PZ)$ and $\# E = O(PN)$.
\begin{proposition}
An assignment $\alpha$ is realizable with partition size $s$ and the redundancy constraints $(\rho_\mathbf{N},\rho_\mathbf{Z})$ if and only if there exists a maximal flow function $f$ in $G$ with total flow $\rho_\mathbf{N}P$, such that the arcs ($\mathbf{x}_{p,z}$,$\mathbf{n}$, 1) used are exactly those for which $p$ is associated to $n$ in $\alpha$.
\end{proposition}
\begin{proof}
Given such flow $f$, we can reconstruct a candidate $\alpha$. In $f$, the flow passing through $\mathbf{p^+}$ and $\mathbf{p^-}$ is $\rho_\mathbf{N}$, and since the outgoing capacity of every $\mathbf{x}_{p,z}$ is 1, every partition is associated to $\rho_\mathbf{N}$ distinct nodes. The fraction $\rho_\mathbf{Z}$ of the flow passing through every $\mathbf{p^+}$ must be spread over as many distinct zones as every arc outgoing from $\mathbf{p^+}$ has capacity 1. So the reconstructed $\alpha$ verifies the redundancy constraints. For every node $n$, the flow between $\mathbf{n}$ and $\mathbf{t}$ corresponds to the number of partitions associated to $n$. By construction of $f$, this does not exceed $\lfloor c_n/s \rfloor$. We assumed that the partition size is $s$, hence this association does not exceed the storage capacity of the nodes.
In the other direction, given an assignment $\alpha$, one can similarly check that the facts that $\alpha$ respects the redundancy constraints, and the storage capacities of the nodes, are necessary condition to construct a maximal flow function $f$.
\end{proof}
\textbf{Implementation remark:} In the flow algorithm, while exploring the graph, we explore the neighbours of every vertex in a random order to heuristically spread the association between nodes and partitions.
\subsubsection*{Algorithm}
With this result mind, we can describe the first step of our algorithm. All divisions are supposed to be integer division.
To compute the maximal flow, we use Dinic's algorithm. Its complexity on general graphs is $O(\#V^2\#E)$, but on graphs with edge capacity bounded by a constant, it turns out to be $O(\#E^{3/2})$. The graph $G$ does not fall in this case since the capacities of the arcs incoming to $\mathbf{t}$ are far from bounded. However, the proof of this complexity works readily for graph where we only ask the edges \emph{not} incoming to the sink $\mathbf{t}$ to have their capacities bounded by a constant. One can find the proof of this claim in \cite[Section 2]{even1975network}.
The dichotomy adds a logarithmic factor $\log(C)$ where $C=\sum_{n \in\mathbf{N}} c_n$ is the total capacity of the cluster. The total complexity of this first function is hence
$O(\#E^{3/2}\log C )= O\big((PN)^{3/2}\log C\big)$.
\subsubsection*{Metrics}
We can display the discrepancy between the computed $s^*$ and the best size we could hope for a given total capacity, that is $C/\rho_\mathbf{N}$.
\subsection{Computation of a candidate assignment}
Now that we have the optimal partition size $s^*$, to compute a candidate assignment, it would be enough to compute a maximal flow function $f$ on $G(s^*)$. This is what we do if there was no previous assignment $\alpha'$.
If there was some $\alpha'$, we add a step that will heuristically help to obtain a candidate $\alpha$ closer to $\alpha'$. to do so, we fist compute a flow function $\tilde{f}$ that uses only the partition-to-node association appearing in $\alpha'$. Most likely, $\tilde{f}$ will not be a maximal flow of $G(s^*)$. In Dinic's algorithm, we can start from a non maximal flow function and then discover improving paths. This is what we do in starting from $\tilde{f}$. The hope\footnote{This is only a hope, because one can find examples where the construction of $f$ from $\tilde{f}$ produces an assignment $\alpha$ that is not as close as possible to $\alpha'$.} is that the final flow function $f$ will tend to keep the associations appearing in $\tilde{f}$.
More formally, we construct the graph $G_{|\alpha'}$ from $G$ by removing all the arcs $(\mathbf{x}_{p,z},\mathbf{n}, 1)$ where $p$ is not associated to $n$ in $\alpha'$. We compute a maximal flow function $\tilde{f}$ in $G_{|\alpha'}$. $\tilde{f}$ is also a valid (most likely non maximal) flow function in $G$. We compute a maximal flow function $f$ on $G$ by starting Dinic's algorithm on $\tilde{f}$.
\State$ f \leftarrow$\Call{Maximal flow from flow}{$G$, $\tilde{f}$}
\State\Return$f$
\EndFunction
\end{algorithmic}
\textbf{Remark:} The function ``Maximal flow'' can be just seen as the function ``Maximal flow from flow'' called with the zero flow function as starting flow.
\subsubsection*{Complexity}
From the consideration of the last section, we have the complexity of the Dinic's algorithm $O(\#E^{3/2})= O((PN)^{3/2})$.
\subsubsection*{Metrics}
We can display the flow value of $\tilde{f}$, which is an upper bound of the distance between $\alpha$ and $\alpha'$. It might be more a Debug level display than Info.
\subsection{Minimization of the transfer load}
Now that we have a candidate flow function $f$, we want to modify it to make its associated assignment as close as possible to $\alpha'$. Denote by $f'$ the maximal flow associated to $\alpha'$, and let $d(f, f')$ be distance between the associated assignments\footnote{It is the number of arcs of type $(\mathbf{x}_{p,z},\mathbf{n})$ saturated in one flow and not in the other.}.
We want to build a sequence $f=f_0, f_1, f_2\dots$ of maximal flows such that $d(f_i, \alpha')$ decreases as $i$ increases. The distance being a non-negative integer, this sequence of flow functions must be finite. We now explain how to find some improving $f_{i+1}$ from $f_i$.
For any maximal flow $f$ in $G$, we define the oriented weighted graph $G_f=(V, E_f)$ as follows. The vertices of $G_f$ are the same as the vertices of $G$. $E_f$ contains the arc $(v_1,v_2, w)$ between vertices $v_1,v_2\in V$ with weight $w$ if and only if the arc $(v_1,v_2)$ is not saturated in $f$ (i.e. $c(v_1,v_2)-f(v_1,v_2)\ge1$, we also consider reversed arcs). The weight $w$ is:
\begin{itemize}
\item$-1$ if $(v_1,v_2)$ is of type $(\mathbf{x}_{p,z},\mathbf{n})$ or $(\mathbf{x}_{p,z},\mathbf{n})$ and is saturated in only one of the two flows $f,f'$;
\item$+1$ if $(v_1,v_2)$ is of type $(\mathbf{x}_{p,z},\mathbf{n})$ or $(\mathbf{x}_{p,z},\mathbf{n})$ and is saturated in either both or none of the two flows $f,f'$;
\item$0$ otherwise.
\end{itemize}
If $\gamma$ is a simple cycle of arcs in $G_f$, we define its weight $w(\gamma)$ as the sum of the weights of its arcs. We can add $+1$ to the value of $f$ on the arcs of $\gamma$, and by construction of $G_f$ and the fact that $\gamma$ is a cycle, the function that we get is still a valid flow function on $G$, it is maximal as it has the same flow value as $f$. We denote this new function $f+\gamma$.
\begin{proposition}
Given a maximal flow $f$ and a simple cycle $\gamma$ in $G_f$, we have $d(f+\gamma, f')- d(f,f')= w(\gamma)$.
\end{proposition}
\begin{proof}
Let $X$ be the set of arcs of type $(\mathbf{x}_{p,z},\mathbf{n})$. Then we can express $d(f,f')$ as
Remark that since we passed on unit of flow in $\gamma$ to construct $f+\gamma$, we have for any $e\in X$, $f(e)=f'(e)$ if and only if $(f+\gamma)(e)\neq f'(e)$.
Plugging this in the previous equation, we find that
$$d(f,f')+w(\gamma)= d(f+\gamma, f').$$
\end{proof}
This result suggests that given some flow $f_i$, we just need to find a negative cycle $\gamma$ in $G_{f_i}$ to construct $f_{i+1}$ as $f_i+\gamma$. The following proposition ensures that this greedy strategy reaches an optimal flow.
\begin{proposition}
For any maximal flow $f$, $G_f$ contains a negative cycle if and only if there exists a maximal flow $f^*$ in $G$ such that $d(f^*, f') < d(f, f')$.
\end{proposition}
\begin{proof}
Suppose that there is such flow $f^*$. Define the oriented multigraph $M_{f,f^*}=(V,E_M)$ with the same vertex set $V$ as in $G$, and for every $v_1,v_2\in V$, $E_M$ contains $(f^*(v_1,v_2)- f(v_1,v_2))_+$ copies of the arc $(v_1,v_2)$. For every vertex $v$, its total degree (meaning its outer degree minus its inner degree) is equal to
The last two sums are zero for any inner vertex since $f,f^*$ are flows, and they are equal on the source and sink since the two flows are both maximal and have hence the same value. Thus, $\deg v =0$ for every vertex $v$.
This implies that the multigraph $M_{f,f^*}$ is the union of disjoint simple cycles. $f$ can be transformed into $f^*$ by pushing a mass 1 along all these cycles in any order. Since $d(f^*, f')<d(f,f')$, there must exists one of these simple cycles $\gamma$ with $d(f+\gamma, f') < d(f, f')$. Finally, since we can push a mass in $f$ along $\gamma$, it must appear in $G_f$. Hence $\gamma$ is a cycle of $G_f$ with negative weight.
\end{proof}
In the next section we describe the corresponding algorithm. Instead of discovering only one cycle, we are allowed to discover a set $\Gamma$ of disjoint negative cycles.
\subsubsection*{Algorithm}
\begin{algorithmic}[1]
\Function{Minimize transfer load}{$G$, $f$, $\alpha'$}
The distance $d(f,f')$ is bounded by the maximal number of differences in the associated assignment. If these assignment are totally disjoint, this distance is $2\rho_N P$. At every iteration of the While loop, the distance decreases, so there is at most $O(\rho_N P)= O(P)$ iterations.
The detection of negative cycle is done with the Bellman-Ford algorithm, whose complexity should normally be $O(\#E\#V)$. In our case, it amounts to $O(P^2ZN)$. Multiplied by the complexity of the outer loop, it amounts to $O(P^3ZN)$ which is a lot when the number of partitions and nodes starts to be large. To avoid that, we adapt the Bellman-Ford algorithm.
The Bellman-Ford algorithm runs $\#V$ iterations of an outer loop, and an inner loop over $E$. The idea is to compute the shortest paths from a source vertex $v$ to all other vertices. After $k$ iterations of the outer loop, the algorithm has computed all shortest path of length at most $k$. All simple paths have length at most $\#V-1$, so if there is an update in the last iteration of the loop, it means that there is a negative cycle in the graph. The observation that will enable us to improve the complexity is the following:
\begin{proposition}
In the graph $G_f$ (and $G$), all simple paths have a length at most $4N$.
\end{proposition}
\begin{proof}
Since $f$ is a maximal flow, there is no outgoing edge from $\mathbf{s}$ in $G_f$. One can thus check than any simple path of length 4 must contain at least two node of type $\mathbf{n}$. Hence on a path, at most 4 arcs separate two successive nodes of type $\mathbf{n}$.
\end{proof}
Thus, in the absence of negative cycles, shortest paths in $G_f$ have length at most $4N$. So we can do only $4N+1$ iterations of the outer loop in Bellman-Ford algorithm. This makes the complexity of the detection of one set of cycle to be $O(N\#E)= O(N^2 P)$.
With this improvement, the complexity of the whole algorithm is, in the worst case, $O(N^2P^2)$. However, since we detect several cycles at once and we start with a flow that might be close to the previous one, the number of iterations of the outer loop might be smaller in practice.
\subsubsection*{Metrics}
We can display the node and zone utilization ratio, by dividing the flow passing through them divided by their outgoing capacity. In particular, we can pinpoint saturated nodes and zones (i.e. used at their full potential).
We can display the distance to the previous assignment, and the number of partition transfers.
\section{Properties of an optimal 3-strict assignment}
\subsection{Optimal assignment}
\label{sec:opt_assign}
For every zone $z\in Z$, define the zone capacity $c_z =\sum_{v, z_v=z} c_v$ and define $C =\sum_v c_v =\sum_z c_z$.
One can check that the best we could be doing to maximize $s^*$ would be to use the nodes proportionally to their capacity. This would yield $s^*=C/(3N)$. This is not possible because of (i) redundancy constraints and (ii) integer rounding but it gives and upper bound.
\subsubsection*{Optimal utilization}
We call an \emph{utilization} a collection of non-negative integers $(n_v)_{v\in V}$ such that $\sum_v n_v =3N$ and for every zone $z$, $\sum_{v\in z} n_v \le N$. We call such utilization \emph{optimal} if it maximizes $s^*$.
We start by computing a node sub-utilization $(\hat{n}_v)_{v\in V}$ such that for every zone $z$, $\sum_{v\in z}\hat{n}_v \le N$ and we show that there is an optimal utilization respecting the constraints and such that $\hat{n}_v \le n_v$ for every node.
Assume that there is a zone $z_0$ such that $c_{z_0}/C \ge1/3$. Then for any $v\in z_0$, we define
which is the universal upper bound on $s^*$. Hence any optimal utilization $(n_v)$ can be modified to another optimal utilization such that $n_v\ge\hat{n}_v$
Because $z_0$ cannot store more than $N$ partition occurences, in any assignment, at least $2N$ partitions must be assignated to the zones $Z\setminus\{z_0\}$. Let $C_0= C-c_{z_0}$. Suppose that there exists a zone $z_1\neq z_0$ such that $c_{z_1}/C_0\ge1/2$. Then, with the same argument as for $z_0$, we can define
Now we can assign the remaining partitions. Let $(\hat{N}, \hat{C})$ to be
\begin{itemize}
\item$(3N,C)$ if we did not find any $z_0$;
\item$(2N,C-c_{z_0})$ if there was a $z_0$ but no $z_1$;
\item$(N,C-c_{z_0}-c_{z_1})$ if there was a $z_0$ and a $z_1$.
\end{itemize}
Then at least $\hat{N}$ partitions must be spread among the remaining zones. Hence $s^*$ is upper bounded by $\hat{C}/\hat{N}$ and without loss of generality, we can define, for every node that is not in $z_0$ nor $z_1$,
We constructed a sub-utilization $\hat{n}_v$. Now notice that $3N-\sum_v \hat{n}_v \le\# V$ where $\# V$ denotes the number of nodes. We can iteratively pick a node $v^*$ such that
\begin{itemize}
\item$\sum_{v\in z_{v^*}}\hat{n}_v < N$ where $z_{v^*}$ is the zone of $v^*$;
\item$v^*$ maximizes the quantity $c_v/(\hat{n}_v+1)$ among the vertices satisfying the first condition (i.e. not in a saturated zone).
\end{itemize}
We iterate these instructions until $\sum_v \hat{n}_v=3N$, and at this stage we define $(n_v)=(\hat{n}_v)$. It is easy to prove by induction that at every step, there is an optimal utilization that is pointwise larger than $\hat{n}_v$, and in particular, that $(n_v)$ is optimal.
\subsubsection*{Existence of an optimal assignment}
As for now, the \emph{optimal utilization} that we obtained is just a vector of numbers and it is not clear that it can be realized as the utilization of some concrete assignment. Here is a way to get a concrete assignment.
Define $3N$ tokens $t_1,\ldots, t_{3N}\in V$ as follows:
\begin{itemize}
\item Enumerate the zones $z$ of $Z$ in any order;
\item enumerate the nodes $v$ of $z$ in any order;
\item repeat $n_v$ times the token $v$.
\end{itemize}
Then for $1\le i \le N$, define the triplet $T_i$ to be
$(t_i, t_{i+N}, t_{i+2N})$. Since the same nodes of a zone appear contiguously, the three nodes of a triplet must belong to three distinct zones.
However simple, this solution to go from an utilization to an assignment has the drawback of not spreading the triplets: a node will tend to be associated to the same two other nodes for many partitions. Hence, during data transfer, it will tend to use only two link, instead of spreading the bandwith use over many other links to other nodes. To achieve this goal, we will reframe the search of an assignment as a flow problem. and in the flow algorithm, we will introduce randomness in the order of exploration. This will be sufficient to obtain a good dispersion of the triplets.
\caption{On the left, the creation of a concrete assignment with the naive approach of repeating tokens. On the right, the zones containing the nodes.}
\end{figure}
\subsubsection*{Assignment as a maximum flow problem}
We describe the flow problem via its graph $(X,E)$ where $X$ is a set of vertices, and $E$ are directed weighted edges between the vertices. For every zone $z$, define $n_z=\sum_{v\in z} n_v$.
The set of vertices $X$ contains the source $\mathbf{s}$ and the sink $\mathbf{t}$; a vertex $\mathbf{x}_z$ for every zone $z\in Z$, and a vertex $\mathbf{y}_i$ for every partition index $1\le i\le N$.
The set of edges $E$ contains
\begin{itemize}
\item the edge $(\mathbf{s}, \mathbf{x}_z, n_z)$ for every zone $z\in Z$;
\item the edge $(\mathbf{x}_z, \mathbf{y}_i, 1)$ for every zone $z\in Z$ and partition $1\le i\le N$;
\item the edge $(\mathbf{y}_i, \mathbf{t}, 3)$ for every partition $1\le i\le N$.
\caption{Flow problem to compute and optimal assignment.}
\end{figure}
We first show the equivalence between this problem and and the construction of an assignment. Given some optimal assignment $(n_v)$, define the flow $f:E\to\mathbb{N}$ that saturates every edge from $\mathbf{s}$ or to $\mathbf{t}$, takes value $1$ on the edge between $\mathbf{x}_z$ and $\mathbf{y}_i$ if partition $i$ is stored in some node of the zone $z$, and $0$ otherwise. One can easily check that $f$ thus defined is indeed a flow and is maximum.
Reciprocally, by the existence of maximum flows constructed from optimal assignments, any maximum flow must saturate the edges linked to the source or the sink. It can only take value 0 or 1 on the other edge, and every partition vertex is associated to exactly three distinct zone vertices. Every zone is associated to exactly $n_z$ partitions.
A maximum flow can be constructed using, for instance, Dinic's algorithm. This algorithm works by discovering augmenting path to iteratively increase the flow. During the exploration of the graph to find augmenting path, we can shuffle the order of enumeration of the neighbours to spread the associations between zones and partitions.
Once we have such association, we can randomly distribute the $n_z$ edges picked for every zone $z$ to its nodes $v\in z$ such that every such $v$ gets $n_z$ edges. This defines an optimal assignment of partitions to nodes.
\subsection{Minimal transfer}
Assume that there was a previous assignment $(T'_i)_{1\le i\le N}$ corresponding to utilizations $(n'_v)_{v\in V}$. We would like the new computed assignment $(T_i)_{1\le i\le N}$ from some $(n_v)_{v\in V}$ to minimize the number of partitions that need to be transferred. We can imagine two different objectives corresponding to different hypotheses:
\begin{equation}
\tag{H3A}
\label{hyp:A}
\text{\emph{Transfers between different zones cost much more than inside a zone.}}
\end{equation}
\begin{equation}
\tag{H3B}
\label{hyp:B}
\text{\emph{Changing zone is not the largest cost when transferring a partition.}}
\end{equation}
In case $A$, our goal will be to minimize the number of changes of zone in the assignment of partitions to zone. More formally, we will maximize the quantity
$$
Q_Z :=
\sum_{1\le i\le N}
\#\{z\in Z ~|~ z\cap T_i \neq\emptyset, z\cap T'_i \neq\emptyset\}
.$$
In case $B$, our goal will be to minimize the number of changes of nodes in the assignment of partitions to nodes. We will maximize the quantity
$$
Q_V :=
\sum_{1\le i\le N}\#(T_i \cap T'_i).
$$
It is tempting to hope that there is a way to maximize both quantity, that having the least discrepancy in terms of nodes will lead to the least discrepancy in terms of zones. But this is actually wrong! We propose the following counter-example to convince the reader:
We consider eight nodes $a, a', b, c, d, d', e, e'$ belonging to five different zones $\{a,a'\}, \{b\}, \{c\}, \{d,d'\}, \{e, e'\}$. We take three partitions ($N=3$), that are originally assigned with some utilization $(n'_v)_{v\in V}$ as follows:
$$
T'_1=(a,b,c) \qquad
T'_2=(a',b,d) \qquad
T'_3=(b,c,e).
$$
This assignment, with updated utilizations $(n_v)_{v\in V}$ minimizes the number of zone changes:
$$
T_1=(d,b,c) \qquad
T_2=(a,b,d) \qquad
T_3=(b,c,e').
$$
This one, with the same utilization, minimizes the number of node changes:
$$
T_1=(a,b,c) \qquad
T_2=(e',b,d) \qquad
T_3=(b,c,d').
$$
One can check that in this case, it is impossible to minimize both the number of zone and node changes.
Because of the redundancy constraint, we cannot use a greedy algorithm to just replace nodes in the triplets to try to get the new utilization rate: this could lead to blocking situation where there is still a hole to fill in a triplet but no available node satisfies the zone separation constraint. To circumvent this issue, we propose an algorithm based on finding cycles in a graph encoding of the assignment. As in section \ref{sec:opt_assign}, we can explore the neigbours in a random order in the graph algorithms, to spread the triplets distribution.
\subsubsection{Minimizing the zone discrepancy}
First, notice that, given an assignment of partitions to \emph{zones}, it is easy to deduce an assignment to \emph{nodes} that minimizes the number of transfers for this zone assignment: For every zone $z$ and every node $v\in z$, pick in any way a set $P_v$ of partitions that where assigned to $v$ in $T'$, to $z_v$ in $T$, with the cardinality of $P_v$ smaller than $n_v$. Once all these sets are chosen, complement the assignment to reach the right utilization for every node. If $\#P_v > n_v$, it means that all the partitions that could stay in $v$ (i.e. that were already in $v$ and are still assigned to its zone) do stay in $v$. If $\#P_v = n_v$, then $n_v$ partitions stay in $v$, which is the number of partitions that need to be in $v$ in the end. In both cases, we could not hope for better given the partition to zone assignment.
Our goal now is to find a assignment of partitions to zones that minimizes the number of zone transfers. To do so we are going to represent an assignment as a graph.
Let $G_T=(X,E_T)$ be the directed weighted graph with vertices $(\mathbf{x}_i)_{1\le i\le N}$ and $(\mathbf{y}_z)_{z\in Z}$. For any $1\le i\le N$ and $z\in Z$, $E_T$ contains the arc:
\begin{itemize}
\item$(\mathbf{x}_i, \mathbf{y}_z, +1)$, if $z$ appears in $T_i'$ and $T_i$;
\item$(\mathbf{x}_i, \mathbf{y}_z, -1)$, if $z$ appears in $T_i$ but not in $T'_i$;
\item$(\mathbf{y}_z, \mathbf{x}_i, -1)$, if $z$ appears in $T'_i$ but not in $T_i$;
\item$(\mathbf{y}_z, \mathbf{x}_i, +1)$, if $z$ does not appear in $T'_i$ nor in $T_i$.
\end{itemize}
In other words, the orientation of the arc encodes whether partition $i$ is stored in zone $z$ in the assignment $T$ and the weight $\pm1$ encodes whether this corresponds to what happens in the assignment $T'$.
\caption{On the left: the graph $G_T$ encoding an assignment to minimize the zone discrepancy. On the right: the graph $G_T$ encoding an assignment to minimize the node discrepancy.}
\end{figure}
Notice that at every partition, there are three outgoing arcs, and at every zone, there are $n_z$ incoming arcs. Moreover, if $w(e)$ is the weight of an arc $e$, define the weight of $G_T$ by
&=\#Z \times N - 4 \sum_{1\le i\le N} 3- \#\{z\in Z ~|~ z\cap T_i \neq\emptyset, z\cap T'_i \neq\emptyset\}\\
&= (\#Z-12)N + 4 Q_Z.
\end{align*}
Hence maximizing $Q_Z$ is equivalent to maximizing $w(G_T)$.
Assume that their exist some assignment $T^*$ with the same utilization $(n_v)_{v\in V}$. Define $G_{T^*}$ similarly and consider the set $E_\mathrm{Diff}= E_T \setminus E_{T^*}$ of arcs that appear only in $G_T$. Since all vertices have the same number of incoming arcs in $G_T$ and $G_{T^*}$, the vertices of the graph $(X, E_\mathrm{Diff})$ must all have the same number number of incoming and outgoing arrows. So $E_\mathrm{Diff}$ can be expressed as a union of disjoint cycles. Moreover, the edges of $E_\mathrm{Diff}$ must appear in $E_{T^*}$ with reversed orientation and opposite weight. Hence, we have
Hence, if $T$ is not optimal, there exists some $T^*$ with $w(G_T) < w(G_{T^*})$, and by the considerations above, there must exist a cycle in $E_\mathrm{Diff}$, and hence in $G_T$, with negative weight. If we reverse the edges and weights along this cycle, we obtain some graph. Since we did not change the incoming degree of any vertex, this is the graph encoding of some valid assignment $T^+$ such that $w(G_{T^+}) > w(G_T)$. We can iterate this operation until there is no other assignment $T^*$ with larger weight, that is until we obtain an optimal assignment.
\subsubsection{Minimizing the node discrepancy}
We will follow an approach similar to the one where we minimize the zone discrepancy. Here we will directly obtain a node assignment from a graph encoding.
Let $G_T=(X,E_T)$ be the directed weighted graph with vertices $(\mathbf{x}_i)_{1\le i\le N}$, $(\mathbf{y}_{z,i})_{z\in Z, 1\le i\le N}$ and $(\mathbf{u}_v)_{v\in V}$. For any $1\le i\le N$ and $z\in Z$, $E_T$ contains the arc:
\begin{itemize}
\item$(\mathbf{x}_i, \mathbf{y}_{z,i}, 0)$, if $z$ appears in $T_i$;
\item$(\mathbf{y}_{z,i}, \mathbf{x}_i, 0)$, if $z$ does not appear in $T_i$.
\end{itemize}
For any $1\le i\le N$ and $v\in V$, $E_T$ contains the arc:
\begin{itemize}
\item$(\mathbf{y}_{z_v,i}, \mathbf{u}_v, +1)$, if $v$ appears in $T_i'$ and $T_i$;
\item$(\mathbf{y}_{z_v,i}, \mathbf{u}_v, -1)$, if $v$ appears in $T_i$ but not in $T'_i$;
\item$(\mathbf{u}_v, \mathbf{y}_{z_v,i}, -1)$, if $v$ appears in $T'_i$ but not in $T_i$;
\item$(\mathbf{u}_v, \mathbf{y}_{z_v,i}, +1)$, if $v$ does not appear in $T'_i$ nor in $T_i$.
\end{itemize}
Every vertex $\mathbb{x}_i$ has outgoing degree 3, every vertex $\mathbf{y}_{z,v}$ has outgoing degree 1, and every vertex $\mathbf{u}_v$ has incoming degree $n_v$.
Remark that any graph respecting these degree constraints is the encoding of a valid assignment with utilizations $(n_v)_{v\in V}$, in particular no partition is stored in two nodes of the same zone.
Exactly like in the previous section, the existence of an assignment with larger weight implies the existence of a negatively weighted cycle in $G_T$. Reversing this cycle gives us the encoding of a valid assignment with a larger weight. Iterating this operation yields an optimal assignment.
\subsubsection{Linear combination of both criteria}
In the graph $G_T$ defined in the previous section, instead of having weights $0$ and $\pm1$, we could be having weights $\pm\alpha$ between $\mathbf{x}$ and $\mathbf{y}$ vertices, and weights $\pm\beta$ between $\mathbf{y}$ and $\mathbf{u}$ vertices, for some $\alpha,\beta>0$ (we have positive weight if the assignment corresponds to $T'$ and negative otherwise). Then
\begin{align*}
w(G_T) &= \sum_{e\in E_T} w(e) =
\alpha\big( (\#Z-12)N + 4 Q_Z\big) +
\beta\big( (\#V-12)N + 4 Q_V\big) \\
&= \mathrm{const}+ 4(\alpha Q_Z + \beta Q_V).
\end{align*}
So maximizing the weight of such graph encoding would be equivalent to maximizing a linear combination of $Q_Z$ and $Q_V$.
\subsection{Algorithm}
We give a high level description of the algorithm to compute an optimal 3-strict assignment. The operations appearing at lines 1,2,4 are respectively described by Algorithms \ref{alg:util},\ref{alg:opt} and \ref{alg:mini}.
\State$T \leftarrow$\Call{Minimization of transfers}{$(T_i)_{1\le i\le N}$, $(T'_i)_{1\le i\le N}$}
\EndIf
\State\Return$T$.
\EndFunction
\end{algorithmic}
\end{algorithm}
We give some considerations of worst case complexity for these algorithms. In the following, we assume $N>\#V>\#Z$. The complexity of Algorithm \ref{alg:total} is $O(N^3\# Z)$ if we assume \eqref{hyp:A} and $O(N^3\#Z \#V)$ if we assume \eqref{hyp:B}.
Algorithm \ref{alg:util} can be implemented with complexity $O(\#V^2)$. The complexity of the function call at line \ref{lin:subutil} is $O(\#V)$. The difference between the sum of the subutilizations and $3N$ is at most the sum of the rounding errors when computing the $\hat{n}_v$. Hence it is bounded by $\#V$ and the loop at line \ref{lin:loopsub} is iterated at most $\#V$ times. Finding the minimizing $v$ at line \ref{lin:findmin} takes $O(\#V)$ operations (naively, we could also use a heap).
Algorithm \ref{alg:opt} can be implemented with complexity $O(N^3\times\#Z)$. The flow graph has $O(N+\#Z)$ vertices and $O(N\times\#Z)$ edges. Dinic's algorithm has complexity $O(\#\mathrm{Vertices}^2\#\mathrm{Edges})$ hence in our case it is $O(N^3\times\#Z)$.
Algorithm \ref{alg:mini} can be implented with complexity $O(N^3\# Z)$ under \eqref{hyp:A} and $O(N^3\#Z \#V)$ under \eqref{hyp:B}.
The graph $G_T$ has $O(N)$ vertices and $O(N\times\#Z)$ edges under assumption \eqref{hyp:A} and respectively $O(N\times\#Z)$ vertices and $O(N\times\#V)$ edges under assumption \eqref{hyp:B}. The loop at line \ref{lin:repeat} is iterated at most $N$ times since the distance between $T$ and $T'$ decreases at every iteration. Bellman-Ford algorithm has complexity $O(\#\mathrm{Vertices}\#\mathrm{Edges})$, which in our case amounts to $O(N^2\# Z)$ under \eqref{hyp:A} and $O(N^2\#Z \#V)$ under \eqref{hyp:B}.
\State Compute the maximal flow $f$ using Dinic's algorithm with randomized neighbours enumeration
\State Construct the assignment $(T_i)_{1\le i\le N}$ from $f$
\State\Return$(T_i)_{1\le i\le N}$
\EndFunction
\end{algorithmic}
\end{algorithm}
\begin{algorithm}
\caption{Minimization of the number of transfers}
\label{alg:mini}
\begin{algorithmic}[1]
\Function{Minimization of transfers}{$(T_i)_{1\le i\le N}$, $(T'_i)_{1\le i\le N}$}
\State Construct the graph encoding $G_T$
\Repeat\label{lin:repeat}
\State Find a negative cycle $\gamma$ using Bellman-Ford algorithm on $G_T$
\State Reverse the orientations and weights of edges in $\gamma$
\Until{no negative cycle is found}
\State Update $(T_i)_{1\le i\le N}$ from $G_T$
\State\Return$(T_i)_{1\le i\le N}$
\EndFunction
\end{algorithmic}
\end{algorithm}
\newpage
\section{Computation of a 3-non-strict assignment}
\subsection{Choices of optimality}
In this mode, we primarily want to store every partition on three nodes, and only secondarily try to spread the nodes among different zone. So we make the choice of not taking the zone repartition in the criterion of optimality.
We try to maximize $s^*$ defined in \eqref{eq:optimal}. So we can compute the optimal utilizations $(n_v)_{v\in V}$ with the only constraint that $n_v \le N$ for every node $v$. As in the previous section, we start with a sub-utilization proportional to $c_v$ (and capped at $N$), and we iteratively increase the $\hat{n}_v$ that is less than $N$ and maximizes the quantity $c_v/(\hat{n}_v+1)$, until the total sum is $3N$.
\subsection{Computation of a candidate assignment}
To compute a candidate assignment (that does not optimize zone spreading nor distance to a previous assignment yet), we can use the folowing flow problem.
Define the oriented weighted graph $(X,E)$. The set of vertices $X$ contains the source $\mathbf{s}$, the sink $\mathbf{t}$, vertices
$\mathbf{x}_p, \mathbf{u}^+_p, \mathbf{u}^-_p$ for every partition $p$, vertices $\mathbf{y}_{p,z}$ for every partition $p$ and zone $z$, and vertices $\mathbf{z}_v$ for every node $v$.
The set of edges is composed of the following arcs:
\begin{itemize}
\item ($\mathbf{s}$,$\mathbf{x}_p$, 3) for every partition $p$;
\item ($\mathbf{x}_p$,$\mathbf{u}^+_p$, 3) for every partition $p$;
\item ($\mathbf{x}_p$,$\mathbf{u}^-_p$, 2) for every partition $p$;
\item ($\mathbf{u}^+_p$,$\mathbf{y}_{p,z}$, 1) for every partition $p$ and zone $z$;
\item ($\mathbf{u}^-_p$,$\mathbf{y}_{p,z}$, 2) for every partition $p$ and zone $z$;
\item ($\mathbf{y}_{p,z}$,$\mathbf{z}_v$, 1) for every partition $p$, zone $z$ and node $v\in z$;
\item ($\mathbf{z}_v$, $\mathbf{t}$, $n_v$) for every node $v$;
\end{itemize}
One can check that any maximal flow in this graph corresponds to an assignment of partitions to nodes. In such a flow, all the arcs from $\mathbf{s}$ and to $\mathbf{t}$ are saturated. The arc from $\mathbf{y}_{p,z}$ to $\mathbf{z}_v$ is saturated if and only if $p$ is associated to~$v$.
Finally the flow from $\mathbf{x}_p$ to $\mathbf{y}_{p,z}$ can go either through $\mathbf{u}^+_p$ or $\mathbf{u}^-_p$.
\subsection{Maximal spread and minimal transfers}
Notice that if the arc $\mathbf{u}_p^+\mathbf{y}_{p,z}$ is not saturated but there is some flow in $\mathbf{u}_p^-\mathbf{y}_{p,z}$, then it is possible to transfer a unit of flow from the path $\mathbf{x}_p\mathbf{u}_p^-\mathbf{y}_{p,z}$ to the path $\mathbf{x}_p\mathbf{u}_p^+\mathbf{y}_{p,z}$. So we can always find an equivalent maximal flow $f^*$ that uses the path through $\mathbf{u}_p^-$ only if the path through $\mathbf{u}_p^+$ is saturated.
We will use this fact to consider the amount of flow going through the vertices $\mathbf{u}^+$ as a measure of how well the partitions are spread over nodes belonging to different zones. If the partition $p$ is associated to 3 different zones, then a flow of 3 will cross $\mathbf{u}_p^+$ in $f^*$ (i.e. a flow of 0 will cross $\mathbf{u}_p^+$). If $p$ is associated to two zones, a flow of $2$ will cross $\mathbf{u}_p^+$. If $p$ is associated to a single zone, a flow of $1$ will cross $\mathbf{u}_p^+$.
Let $N_1, N_2, N_3$ be the number of partitions associated to respectively 1,2 and 3 distinct zones. We will optimize a linear combination of these variables using the discovery of positively weighted circuits in a graph.
At the same step, we will also optimize the distance to a previous assignment $T'$. Let $\alpha> \beta> \gamma\ge0$ be three parameters.
Given the flow $f$, let $G_f=(X',E_f)$ be the multi-graph where $X' = X\setminus\{\mathbf{s},\mathbf{t}\}$. The set $E_f$ is composed of the arcs:
\begin{itemize}
\item As many arcs from $(\mathbf{x}_p, \mathbf{u}^+_p,\alpha), (\mathbf{x}_p, \mathbf{u}^+_p,\beta), (\mathbf{x}_p, \mathbf{u}^+_p,\gamma)$ (selected in this order) as there is flow crossing $\mathbf{u}^+_p$ in $f$;
\item As many arcs from $(\mathbf{u}^+_p, \mathbf{x}_p,-\gamma), (\mathbf{u}^+_p, \mathbf{x}_p,-\beta), (\mathbf{u}^+_p, \mathbf{x}_p,-\alpha)$ (selected in this order) as there is flow crossing $\mathbf{u}^-_p$ in $f$;
\item As many copies of $(\mathbf{x}_p, \mathbf{u}^-_p,0)$ as there is flow through $\mathbf{u}^-_p$;
\item As many copies of $(\mathbf{u}^-_p,\mathbf{x}_p,0)$ so that the number of arcs between these two vertices is 2;
\item$(\mathbf{u}^+_p,\mathbf{y}_{p,z}, 0)$ if the flow between these vertices is 1, and the opposite arc otherwise;
\item as many copies of $(\mathbf{u}^-_p,\mathbf{y}_{p,z}, 0)$ as the flow between these vertices, and as many copies of the opposite arc as 2~$-$~the flow;
\item$(\mathbf{y}_{p,z},\mathbf{z}_v, \pm1)$ if it is saturated in $f$, with $+1$ if $v\in T'_p$ and $-1$ otherwise;
\item$(\mathbf{z}_v,\mathbf{y}_{p,z}, \pm1)$ if it is not saturated in $f$, with $+1$ if $v\notin T'_p$ and $-1$ otherwise.
\end{itemize}
To summarize, arcs are oriented left to right if they correspond to a presence of flow in $f$, and right to left if they correspond to an absence of flow. They are positively weighted if we want them to stay at their current state, and negatively if we want them to switch. Let us compute the weight of such graph.
As for the mode 3-strict, one can check that the difference of two such graphs corresponding to the same $(n_v)$ is always eulerian. Hence we can navigate in this class with the same greedy algorithm that discovers positive cycles and flips them.
The function that we optimize is
$$
2Q_V + \beta N_2 + (\beta+\gamma) N_3.
$$
The choice of parameters $\beta$ and $\gamma$ should be lead by the following question: For $\beta$, where to put the tradeoff between zone dispersion and distance to the previous configuration? For $\gamma$, do we prefer to have more partitions spread between 2 zones, or have less between at least 2 zones but more between 3 zones.
The quantity $Q_V$ varies between $0$ and $3N$, it should be of order $N$. The quantity $N_2+N_3$ should also be of order $N$ (it is exactly $N$ in the strict mode). So the two terms of the function are comparable.
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