We give a polynomial algorithm to compute shortest paths in weighted undirected graphs with no negative cycles (conservative graphs). We show that our procedure gives a simple algorithm to compute optimal T-joins (and consequently all of their special cases, including weighted matchings). We finally give a direct algorithmic proof for arbitrary weights of a theorem of Sebo ̋ characterizing conservative graphs and optimal paths.
Shortest Paths in Conservative Graphs
RIZZI, ROMEO
2001-01-01
Abstract
We give a polynomial algorithm to compute shortest paths in weighted undirected graphs with no negative cycles (conservative graphs). We show that our procedure gives a simple algorithm to compute optimal T-joins (and consequently all of their special cases, including weighted matchings). We finally give a direct algorithmic proof for arbitrary weights of a theorem of Sebo ̋ characterizing conservative graphs and optimal paths.
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