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

Authors:
Ivona Bezáková;Adam J. Friedlander
Affiliations:
Rochester Institute of Technology, Rochester, NY;IBM, Poughkeepsie, NY
Venue:
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Year:
2010

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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 s-t path in the corresponding unweighted graph. Previously, Ball and Provan gave a polynomial-time algorithm for unweighted 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 image segmentation and other computer vision problems.