Elsevier

Theoretical Computer Science

Volume 417, 3 February 2012, Pages 2-11
Theoretical Computer Science

Counting and sampling minimum (s,t)-cuts in weighted planar graphs in polynomial time

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Abstract

We give an O(nd+nlogn) algorithm computing the number of minimum (s,t)-cuts in weighted planar graphs, where n is the number of vertices and d is the length of the shortest st path in the corresponding unweighted graph. Previously, Ball and Provan gave a polynomial-time algorithm for unweighted planar graphs with both s and t lying on the outer face. Our results hold for all locations of s and t and weighted graphs, and have direct applications in computer vision.

Keywords

Counting and sampling
Minimum (s,t)-cuts
Weighted planar graphs
Maximum flow
Maximal antichains in partially ordered sets

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