Make any coloring algorithm compatible with SMC

[gdalle]

Fixes #67

Context

At the moment, DI can only use algorithms from SMC, but people might want to code other coloring algorithms following the ADTypes interface, for instance our friend @SouthEndMusic who was interested in provably optimal colorings. During decompression, we will still need SMC result types, but those are deeply tied to the coloring algorithm itself (for star and acyclic colorings + their bidirectional counterparts). How do we create SMC results from a generic algorithm which outputs only a vector of colors?

Idea

Pretend we run the greedy algorithm, but force the color choices and piggyback on the rest of the procedure for constructing data structures like the StarSet and TreeSet. This enables maximum code reuse, even though it may not be optimal from a performance standpoint.
As a side bonus, this also allows us to assert correctness of the provided colorings, because our greedy procedure enforces it.

Todo

• Test on a non-trivial coloring algorithm (not just ADTypes.NoColoringAlgorithm) => done with OptimalColoringAlgorithm based on a JuMP formulation, but removed from the current PR
• Solve Add more coloring options -- bicoloring SciML/ADTypes.jl#69 and then integrate that
• Figure out whether we can accept zero (unused) colors in the output of ADTypes.symmetric_coloring or ADTypes.bidirectional_coloring

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (e77226a) to head (e4dd8c1).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##              main      #263   +/-   ##
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  Coverage   100.00%   100.00%           
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  Files           17        17           
  Lines         1955      1962    +7     
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+ Hits          1955      1962    +7     

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[amontoison]

The diff is quite big, it will be hard to review it soon.
Can you ping me when it is ready?

[gdalle]

@amontoison I removed the OptimalColoringAlgorithm part to simplify, this is ready to go

[gdalle]

Gentle bump @amontoison, this one is ready for you while #267 marinates.

PS: I deactivated the formatting test because it passes locally and I can't figure out what's wrong. More generally, JuliaFormatter seems less and less reliable, so I'll soon switch to Runic anyway.

[amontoison]

I will have a look today. I got a visitor last week at ANL that stayed at home. I should be less busy this week!

[gdalle]

Also it seems the GPU tests are failing for unrelated reasons

[amontoison]

Also it seems the GPU tests are failing for unrelated reasons

We ordered a new SSD for Moonshot, it is the issue.

[amontoison]

All tests passed, you can merge it when it is good for you 👍