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Update NC k shortest simple path for Undirected graphs #40547

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Merged
merged 9 commits into from
Aug 16, 2025
Merged

Update NC k shortest simple path for Undirected graphs #40547

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42a2bd7
fix bugs of pnc algorithm
kappybar Jul 30, 2025
0ac4e57
improve implementation of feng algorithm
kappybar Jul 30, 2025
e0528b7
returned weight may be fractional
kappybar Jul 31, 2025
8f09ea2
feng, pnc have common codes
kappybar Aug 1, 2025
845f7e3
integrate Feng, pnc into one function
kappybar Aug 2, 2025
dfa5625
keep feng, pnc algorithm and minor fix
kappybar Aug 2, 2025
2e0b083
update nc_k_shortest_simple_paths for undirected graphs
kappybar Aug 6, 2025
2adbad9
minor fix of nc_k_shortest_simple_paths
kappybar Aug 8, 2025
7fb197d
update docs of shortest_simple_paths
kappybar Aug 8, 2025
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22 changes: 11 additions & 11 deletions src/sage/graphs/cycle_enumeration.py
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Original file line number Diff line number Diff line change
Expand Up @@ -265,11 +265,11 @@ def _all_simple_cycles_iterator_edge(self, edge, max_length=None,
sage: g = graphs.Grid2dGraph(2, 5).to_directed()
sage: it = g._all_simple_cycles_iterator_edge(((0, 0), (0, 1), None), report_weight=True)
sage: for i in range(5): print(next(it))
(2, [(0, 0), (0, 1), (0, 0)])
(4, [(0, 0), (0, 1), (1, 1), (1, 0), (0, 0)])
(6, [(0, 0), (0, 1), (0, 2), (1, 2), (1, 1), (1, 0), (0, 0)])
(8, [(0, 0), (0, 1), (0, 2), (0, 3), (1, 3), (1, 2), (1, 1), (1, 0), (0, 0)])
(10, [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 4), (1, 3), (1, 2), (1, 1), (1, 0), (0, 0)])
(2.0, [(0, 0), (0, 1), (0, 0)])
(4.0, [(0, 0), (0, 1), (1, 1), (1, 0), (0, 0)])
(6.0, [(0, 0), (0, 1), (0, 2), (1, 2), (1, 1), (1, 0), (0, 0)])
(8.0, [(0, 0), (0, 1), (0, 2), (0, 3), (1, 3), (1, 2), (1, 1), (1, 0), (0, 0)])
(10.0, [(0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 4), (1, 3), (1, 2), (1, 1), (1, 0), (0, 0)])

The function works for undirected graphs as well::

Expand Down Expand Up @@ -841,12 +841,12 @@ def all_simple_cycles(self, starting_vertices=None, rooted=False,
sage: cycles_B = g.all_simple_cycles(weight_function=lambda e:e[0]+e[1], by_weight=True,
....: report_weight=True, algorithm='B')
sage: cycles_B
[(2, [0, 1, 0]), (4, [0, 2, 0]), (6, [0, 1, 2, 0]), (6, [0, 2, 1, 0]),
(6, [0, 3, 0]), (6, [1, 2, 1]), (8, [0, 1, 3, 0]), (8, [0, 3, 1, 0]),
(8, [1, 3, 1]), (10, [0, 2, 3, 0]), (10, [0, 3, 2, 0]), (10, [2, 3, 2]),
(12, [0, 1, 3, 2, 0]), (12, [0, 1, 2, 3, 0]), (12, [0, 2, 3, 1, 0]),
(12, [0, 2, 1, 3, 0]), (12, [0, 3, 2, 1, 0]), (12, [0, 3, 1, 2, 0]),
(12, [1, 2, 3, 1]), (12, [1, 3, 2, 1])]
[(2.0, [0, 1, 0]), (4.0, [0, 2, 0]), (6.0, [0, 1, 2, 0]), (6.0, [0, 2, 1, 0]),
(6.0, [0, 3, 0]), (6.0, [1, 2, 1]), (8.0, [0, 1, 3, 0]), (8.0, [0, 3, 1, 0]),
(8.0, [1, 3, 1]), (10.0, [0, 2, 3, 0]), (10.0, [0, 3, 2, 0]), (10.0, [2, 3, 2]),
(12.0, [0, 1, 3, 2, 0]), (12.0, [0, 1, 2, 3, 0]), (12.0, [0, 2, 3, 1, 0]),
(12.0, [0, 2, 1, 3, 0]), (12.0, [0, 3, 2, 1, 0]), (12.0, [0, 3, 1, 2, 0]),
(12.0, [1, 2, 3, 1]), (12.0, [1, 3, 2, 1])]
sage: cycles.sort() == cycles_B.sort()
True

Expand Down
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