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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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51 changes: 30 additions & 21 deletions src/sage/graphs/path_enumeration.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -471,13 +471,6 @@ def shortest_simple_paths(self, source, target, weight_function=None,
('101', '011', 1),
('011', '111', 1)])]

Feng's algorithm cannot be used on undirected graphs::

sage: list(graphs.PathGraph(2).shortest_simple_paths(0, 1, algorithm='Feng'))
Traceback (most recent call last):
...
ValueError: Feng's algorithm works only for directed graphs

If the algorithm is not implemented::

sage: list(g.shortest_simple_paths(1, 5, algorithm='tip top'))
Expand Down Expand Up @@ -528,7 +521,7 @@ def shortest_simple_paths(self, source, target, weight_function=None,
sage: s == t
True

Check that "Yen" and "Feng" provide same results on random digraphs::
Check that "Yen", "Feng" and "PNC" provide same results on random digraphs::

sage: G = digraphs.RandomDirectedGNP(30, .05)
sage: while not G.is_strongly_connected():
Expand All @@ -546,6 +539,24 @@ def shortest_simple_paths(self, source, target, weight_function=None,
....: raise ValueError(f"something goes wrong u={u}, v={v}, G={G.edges()}!")
....: if i == 100:
....: break

Check that "Yen", "Feng" and "PNC" provide same results on random undirected graphs::

sage: from sage.graphs.generators.random import RandomGNP
sage: G = RandomGNP(30, .05)
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you could simply use G = graphs.RandomGNP(30, .05).

Also, consider increasing the number of edges. With p=0.05 the graph has roughly 20 edges.

sage: for u, v in list(G.edges(labels=False, sort=False)):
....: G.set_edge_label(u, v, randint(1, 10))
sage: V = G.vertices(sort=False)
sage: shuffle(V)
sage: u, v = V[:2]
sage: it_Y = G.shortest_simple_paths(u, v, by_weight=True, report_weight=True, algorithm='Yen')
sage: it_F = G.shortest_simple_paths(u, v, by_weight=True, report_weight=True, algorithm='Feng')
sage: it_P = G.shortest_simple_paths(u, v, by_weight=True, report_weight=True, algorithm='PNC')
sage: for i, (y, f, p) in enumerate(zip(it_Y, it_F, it_P)):
....: if y[0] != f[0] or y[0] != p[0]:
....: raise ValueError(f"something goes wrong u={u}, v={v}, G={G.edges()}!")
....: if i == 100:
....: break
"""
if source not in self:
raise ValueError("vertex '{}' is not in the graph".format(source))
Expand All @@ -569,9 +580,6 @@ def shortest_simple_paths(self, source, target, weight_function=None,
algorithm = "Feng" if self.is_directed() else "Yen"

if algorithm in ("Feng", "PNC"):
if not self.is_directed():
raise ValueError(f"{algorithm}'s algorithm works only for directed graphs")

yield from nc_k_shortest_simple_paths(self, source=source, target=target,
weight_function=weight_function,
by_weight=by_weight, check_weight=check_weight,
Expand Down Expand Up @@ -897,8 +905,6 @@ def nc_k_shortest_simple_paths(self, source, target, weight_function=None,
Return an iterator over the simple paths between a pair of vertices in
increasing order of weights.

Works only for directed graphs.

For unweighted graphs, paths are returned in order of increasing number
of edges.

Expand Down Expand Up @@ -1001,6 +1007,14 @@ def nc_k_shortest_simple_paths(self, source, target, weight_function=None,
(40.0, [(1, 2, 20), (2, 5, 20)]),
(60.0, [(1, 4, 30), (4, 5, 30)])]

Algorithm works for undirected graphs as well::

sage: g = Graph([(1, 2, 20), (1, 3, 10), (1, 4, 30), (2, 5, 20), (3, 5, 10), (4, 5, 30)])
sage: list(nc_k_shortest_simple_paths(g, 5, 1, by_weight=True))
[[5, 3, 1], [5, 2, 1], [5, 4, 1]]
sage: list(nc_k_shortest_simple_paths(g, 5, 1))
[[5, 2, 1], [5, 4, 1], [5, 3, 1]]
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The order in which the paths are reported may not always be the same. To make the test robust, you could report the length of the paths.

sage: [len(P) for P in nc_k_shortest_simple_paths(g, 5, 1)]
[3, 3, 3]

the alternative is to use a lexicographic sorting of the paths

sage: sorted(nc_k_shortest_simple_paths(g, 5, 1))
[[5, 2, 1], [5, 3, 1], [5, 4, 1]]


TESTS::

sage: from sage.graphs.path_enumeration import nc_k_shortest_simple_paths
Expand Down Expand Up @@ -1150,9 +1164,6 @@ def nc_k_shortest_simple_paths(self, source, target, weight_function=None,
sage: for i in range(len(A) - 1):
....: assert A[i] <= A[i + 1]
"""
if not self.is_directed():
raise ValueError("this algorithm works only for directed graphs")

if source not in self:
raise ValueError("vertex '{}' is not in the graph".format(source))
if target not in self:
Expand All @@ -1163,9 +1174,11 @@ def nc_k_shortest_simple_paths(self, source, target, weight_function=None,
return

if self.has_loops() or self.allows_multiple_edges():
G = self.to_simple(to_undirected=False, keep_label='min', immutable=False)
G = self.to_simple(to_undirected=self.is_directed(), keep_label='min', immutable=False)
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Here you force conversion to undirected graph. This seems wrong.

else:
G = self.copy(immutable=False)
if not G.is_directed():
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we can sometimes save a copy

if self.has_loops() or self.allows_multiple_edges():
    G = self.to_simple(to_undirected=False, keep_label='min', immutable=False)
    if not G.is_directed():
        G = G.to_directed()
elif not self.is_directed():
    # Turn the graph into a mutable directed graph
    G = self.to_directed(data_structure='sparse')
else:
    G = self.copy(immutable=False)

G = G.to_directed()

G.delete_edges(G.incoming_edges(source, labels=False))
G.delete_edges(G.outgoing_edges(target, labels=False))
Expand Down Expand Up @@ -1416,8 +1429,6 @@ def feng_k_shortest_simple_paths(self, source, target, weight_function=None,
Return an iterator over the simple paths between a pair of vertices in
increasing order of weights.

Works only for directed graphs.

For unweighted graphs, paths are returned in order of increasing number
of edges.

Expand Down Expand Up @@ -1487,8 +1498,6 @@ def pnc_k_shortest_simple_paths(self, source, target, weight_function=None,
Return an iterator over the simple paths between a pair of vertices in
increasing order of weights.

Works only for directed graphs.

In case of weighted graphs, negative weights are not allowed.

If ``source`` is the same vertex as ``target``, then ``[[source]]`` is
Expand Down
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