(Previously published) Hypper: Using a MaxSAT for resolving chart dependencies on K8s

This article was written by Christian Richter and Víctor Cuadrado Juan, and previously published in community.suse.com


Hypper is a Kubernetes package manager based on Helm. It handles charts in a similar way as Helm does, with a twist: it tries to resolve dependencies between charts to reuse existing resources and deployments. For more info, see the two articles on this blog by @mattfarina: Introducing Hypper and Hypper v3 - Now with a SAT solver.

Hypper is designed to work with shared dependencies: dependencies installed once on a cluster that several charts depend on. Think of Hypper as bringing the usual Linux package management to Kubernetes Helm charts.

Checking all the charts to see if their dependencies are correctly installed or there are some missing is not an easy task. This is called a “Satisfiability problem”, or SAT, for friends. In fact, solving a SAT problem is an NP-Complete problem!.

How to solve a SAT problem?

Finding a solution to that problem may be somewhat easy by reducing the problem space (like Go modules), or using custom heuristics to be fast but without an assurance of finding an optimal solution (like Apt).

To find an optimal solution to a SAT problem fast enough so it’s useful to use, we need a focused approach. That comes from a SAT solver algorithm: it gets fed with facts of a problem, and it finds the optimal combination of facts that can satisfy the problem or a demonstration that such combination doesn’t exist.

In Hypper’s case, we also want the possibility to depend on Helm charts outside of our curated repositories. Therefore, we would benefit from knowing if a system can be upgraded or not, regardless of our ability on curating the repositories. Hence, we use a SAT solver directly when performing those upgrades.

What kinds of SAT solvers exist?

Let’s walk through an example on the following paragraphs and see. We will use the example of installing Wordpress with a dependency to Mariadb (the names are just placeholders for a potential real-life scenario).

Pure SAT

A Pure SAT is the simplest implementation of a SAT solver. It receives first-order logic statements (facts). For example, a fact specifying that Wordpress depends on Mariadb would be not(Wordpress) or Mariadb.

The SAT solver will tell you if there’s a combination of facts that work together (are satisfiable, for example you can install Wordpress because Mariadb is already present), or if there’s no solution, and why.

Pure SAT solvers give you a solution on which dependencies you need to install (several versions of Mariadb for example), or walk around conflicts on several charts (Mariadb conflicts with Mysql), but one still needs to write their own heuristics to pick the suitable versions.

An example of a package manager using a Pure SAT solver is Zypper).

Pseudo-Boolean SAT

In addition to the normal “hard” clauses of a Pure SAT solver, a Pseudo-Boolean SAT operates with soft Pseudo-Boolean equations. In our example, the Pseudo-Boolean equation specifying that Wordpress depends on Mariadb would be:

Mariadb - Wordpress >= 0

There, Mysql and Mariadb can be 1 (installed) or 0 (not installed).

If you want to install Wordpress (Wordpress is 1):

Mariadb - Wordpress >= 0  ; 
Mariadb - 1         >= 0  ; 
Mariadb >= 0 + 1          ;
Mariadb >= 1              ;
Mariadb =  1

In words, Mariadb needs to be installed.

These equations allow to easily list several dependencies:

Mariadb + Mysql - Wordpress >= 0

Pseudo-Boolean SAT solvers simplify even more solving dependencies on several charts, (several versions of Mariadb for example), but one needs still needs to write their own heuristics to pick the suitable versions.


MaxSAT solvers are a generalization of Pseudo-Boolean ones. These kind of solvers allow you to add weights to constraints in the equations, and give you the result that maximizes your preferences. A MaxSAT solver can even find a maximal possible partial solution when there’s no solution for the whole input set.

This turns out to be an even more complex problem, NP-Hard.

An example of using a MaxSAT equation to install Wordpress and its dependency Mariadb on the latest Semver version would be:

max( (Mariadb, version: 10.5.9,  weight: 1) + 
     (Mariadb, version: 10.5.10, weight: 2) + 
     (Mariadb, version: 10.5.11, weight: 3)   )
  - Wordpress >= 0

Why pick MaxSAT?

In our case, we have several strategies we want to apply to our problem:

  • Minimize package removal. The changes to the cluster should be as minimal as possible but as efficient as needed. This does not mean that we are going to have stale deployments on our clusters, but that there will be no package removals when an existing deployment still can fullfill the requirements.
  • Minimize number of package charts. The goal is to have as few deployments on the cluster as needed without cluttering the cluster with unneeded deployments.
  • Maximize freshness of packages. By assigning a distance between package versions, we can optimize for those that have the smaller distance. Doing a full upgrade of the system means selecting to maximize freshness of all installed packages, without asking for installing new packages by default (but allowing for packages to be pulled into the installed list).
  • Minimize install of optional packages. Only install the optional dependencies users actually need, no one likes cluttered systems.
  • Maximize install of optional packages. Install all optional dependencies, useful for test-systems.
  • Minimize changes to installed packages: Configuration changes in values.yaml, treat charts with K8s CRDs differently, etc.

With a MaxSAT solver, we can tackle those. For example we can have certain preferences set by weighting them and solve for the following criteria:

  • Upgrade and minimize changes to installed packages.
  • Upgrade only up to minor or patch Semver versions.
  • Install with the minimum set of dependencies required.

Usually such problems are computationally more intensive than using a normal SAT. But since we have an overseeable problem space (10^1 charts instead of 10^3 packages), we still can manage to solve this in an acceptable time frame.

And how does this look?

Here is Hypper installing Wordpress, with its dependency on Mariadb and an optional dependency on Prometheus. Prometheus has an optional dependency on Grafana, which is already installed.

$ hypper shared-dep list path/to/local/chart/prometheus
grafana  ^8.0.0  https://our-hypper-charts/repo   installed   grafana     shared-optional

$ hypper install path/to/local/chart/wordpress_with_mariadb_and_grafana
❓ Install optional shared dependency "prometheus" of chart "wordpress"? [Y/n]:
The following charts are going to be installed:
wordpress v5.8.0
 ├─ mariadb v10.5.11
 └─ prometheus v2.27.1

🛳  Installing chart "mariadb" as "mariadb" in namespace "databases"…
🛳  Installing chart "prometheus" as "prometheus" in namespace "metrics"…
🛳  Installing chart "wordpress" as "wordpress" in namespace "wordpress"…
👏 Done!

If you are left hungry for a more mathematical explanation, have a look at our docs on this topic here.

Víctor Cuadrado Juan

I'm Víctor Cuadrado Juan, a developer and FOSS enthusiast, in love with Linux. Currently living in Nürnberg, Germany. Feel free to waste your precious time around here, or to contact me.