Implementation of algorithm for exact counting graph homomorphisms

[guojing0]

In the past few months, we have been working towards a SageMath library for exact counting graph homomorphisms, based on the proof of Prop. 1.6 from "Homomorphisms Are a Good Basis for Counting Small Subgraphs" by Radu Curticapean, Holger Dell, and Dániel Marx: The algorithm is deterministic and runs in time $\exp(O(k)) + poly(k) \cdot n^{tw(H) + 1}$ for counting the number of homomorphisms from graph $H$ to graph $G$, where $k = |V(H)|$, $n = |V(G)|$, and $tw(H)$ is the treewidth of $H$.

The library is recently released on GitHub: https://github.com/guojing0/count-graph-homs

This commit is mainly for the sake of CI. More documentations and tests will follow.

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• I have created tests covering the changes.
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[dcoudert]

This PR requires some work before. It must be properly documented, doctests are needed, etc. Here is a first list of needed changes.

I don't think we need this helper_functions.py file. I fact, I'm in favor of using a single file called homomorphisms.py and gathering all methods related to graph homomorphisms.

[dcoudert]

The method don't extract but returns an index

[guojing0]

I belive this returns that vertex at some index

[dcoudert]

The method don't insert but returns the index where to do so.

[guojing0]

Yes, but I could not think of a better name for this. Do you have any name suggestions?

[guojing0]

This PR requires some work before. It must be properly documented, doctests are needed, etc. Here is a first list of needed changes.

Thank you for all the reviews! Of course, many tests and much documentation are needed.

I don't think we need this helper_functions.py file. I fact, I'm in favor of using a single file called homomorphisms.py and gathering all methods related to graph homomorphisms.

I also consider the possibility of having only one file, but wouldn't it make the main file count_homomorphisms.py too long? It's already 230+ lines.

I think the name count_homomorphisms.py would better reflect what the goal(s) this file intends to achieve, i.e., counting homomorphisms; homomorphisms.py sounds somewhat general.

[dcoudert]

I also consider the possibility of having only one file, but wouldn't it make the main file count_homomorphisms.py too long? It's already 230+ lines.

We already have files with 20.000+ lines.

[guojing0]

@dcoudert Thank you again for the code reviews! I think I have changed some codes based on your review.

Do you think we also need examples/tests for the small helper functions at the end of the file?

[dcoudert]

Tests are needed in all methods, even the small helper functions.