Improve method _ford fulkerson chronicle in src/sage/combinat/posets/posets.py

[dcoudert]

We relabel the internal digraph to integers in range 0..n-1 and associate each edge an index in range 0..m-1 to use less dictionaries.

We also do some minor changes in posets.py.

📝 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 accordingly.

⌛ Dependencies

[dcoudert]

An intriguing question is that posets are sometimes created using an immutable digraph and sometimes not. Should we unify that ?

[github-actions]

Documentation preview for this PR (built with commit 58b8506; changes) is ready! 🎉

[fchapoton]

ca m'a l'air correct. C'est plus rapide ?

[dcoudert]

ca m'a l'air correct. C'est plus rapide ?

Dans mes petits tests c'est mieux mais pas une révolution. Il faudrait voir avec des exemples plus gros.

With the example of the doctest:

sage: from sage.combinat.posets.posets import _ford_fulkerson_chronicle
sage: G = DiGraph({1: [3, 6, 7], 2: [4], 3: [7], 4: [], 6: [7, 8],
....:              7: [9], 8: [9, 12], 9: [], 10: [], 12: []})
sage: s = 1
sage: t = 9
sage: (1, 6, None) in G.edges(sort=False)
True
sage: (1, 6) in G.edges(sort=False)
False
sage: a = {(1, 6): 4, (2, 4): 0, (1, 3): 4, (1, 7): 1, (3, 7): 6,
....:      (7, 9): 1, (6, 7): 3, (6, 8): 1, (8, 9): 0, (8, 12): 2}
sage: def B(G, s, t, a, n):
....:     ffc = _ford_fulkerson_chronicle(G, s, t, a)
....:     for _ in range(n):
....:         _ = next(ffc)

Before:

sage: %time B(G, s, t, a, 10)
CPU times: user 560 µs, sys: 86 µs, total: 646 µs
Wall time: 649 µs
sage: %time B(G, s, t, a, 100)
CPU times: user 3.54 ms, sys: 0 ns, total: 3.54 ms
Wall time: 3.54 ms
sage: %time B(G, s, t, a, 1000)
CPU times: user 20.9 ms, sys: 765 µs, total: 21.7 ms
Wall time: 21 ms

After

sage: %time B(G, s, t, a, 10)
CPU times: user 310 µs, sys: 131 µs, total: 441 µs
Wall time: 443 µs
sage: %time B(G, s, t, a, 100)
CPU times: user 1.77 ms, sys: 22 µs, total: 1.79 ms
Wall time: 1.79 ms
sage: %time B(G, s, t, a, 1000)
CPU times: user 12.7 ms, sys: 459 µs, total: 13.1 ms
Wall time: 12.7 ms