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maximum-weight-matching
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Eliminate edges with negative weight 

The base algorithm transparently ignores edges, but only if
the graph contains at least 1 edge with positive weight.
If ALL edges have negative weight, dual variables may be
initialized to negative values which leads to failure.
This commit is contained in:
Joris van Rantwijk 2023-02-06 12:35:35 +01:00
parent 99bc2912d8
commit 23c3e35865
1 changed files with 7 additions and 3 deletions
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10
python/max_weight_matching.py
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@ -28,9 +28,7 @@ def maximum_weight_matching(
Isolated vertices (not incident to any edge) are allowed, but not
recommended since such vertices consume time and memory but have
no effect on the maximum-weight matching.
Negative edge weights are allowed, but not recommended since such edges
consume time and memory but have no effect on the maximum-weight matching.
Edges with negative weight are ignored.
This function takes time O(n**3), where "n" is the number of vertices.
This function uses O(n + m) memory, where "m" is the number of edges.
@ -53,6 +51,12 @@ def maximum_weight_matching(
_check_input_types(edges)
_check_input_graph(edges)
# Eliminate edges with negative weight.
# This does not change the solution but prevents complications
# in the algorithm.
if any(e[2] < 0 for e in edges):
edges = [e for e in edges if e[2] >= 0]
# Special case for empty graphs.
if not edges:
return []