improve graph traversal methods

[dcoudert]

Similarly to #39216, we avoid the conversion to short_digraph when the input graph is an instance of StaticSparseBackend.

Furthermore, we use the new PairingHeap_of_n_integers data structure (#39046) instead of a priority_queue to emulate a max-heap. This is slightly faster this way and cleaner.

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

⌛ Dependencies

[dcoudert]

Some timings to see the (small) advantage of using the pairing heap data structure.

Before

sage: G = graphs.PathGraph(4)
sage: %timeit G.maximum_cardinality_search(initial_vertex=0)
9.77 µs ± 16.9 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
sage: G = graphs.Grid2dGraph(10, 10)
sage: %timeit G.maximum_cardinality_search()
209 µs ± 1.53 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
sage: G = graphs.Grid2dGraph(100, 100)
sage: %timeit G.maximum_cardinality_search()
87.2 ms ± 462 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
sage: G = graphs.CompleteGraph(10)
sage: %timeit G.maximum_cardinality_search()
27 µs ± 85.9 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
sage: G = graphs.Cell600()
sage: %timeit G.maximum_cardinality_search()
355 µs ± 1.6 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)

With this PR:

sage: G = graphs.PathGraph(4)
sage: %timeit G.maximum_cardinality_search(initial_vertex=0)
9.74 µs ± 32.6 ns per loop (mean ± std. dev. of 7 runs, 100,000 loops each)
sage: G = graphs.Grid2dGraph(10, 10)
sage: %timeit G.maximum_cardinality_search()
206 µs ± 371 ns per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
sage: G = graphs.Grid2dGraph(100, 100)
sage: %timeit G.maximum_cardinality_search()
85.9 ms ± 363 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
sage: G = graphs.CompleteGraph(10)
sage: %timeit G.maximum_cardinality_search()
25.4 µs ± 36.5 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)
sage: G = graphs.Cell600()
sage: %timeit G.maximum_cardinality_search()
324 µs ± 1.2 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)

[github-actions]

Documentation preview for this PR (built with commit 438865c; changes) is ready! 🎉
This preview will update shortly after each push to this PR.

[tscrim]

LGTM.

[dcoudert]

Thank you for the review.