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

Authors:
Ivona Bezáková;Adam J. Friedlander
Affiliations:
Rochester Institute of Technology, Rochester, NY, USA;IBM, Poughkeepsie, NY, USA
Venue:
Theoretical Computer Science
Year:
2012

Citing 8
Cited 1

Random generation of combinatorial structures from a uniform

Theoretical Computer Science
Counting almost minimum cutsets with reliability applications

Mathematical Programming: Series A and B
A new approach to the maximum-flow problem

Journal of the ACM (JACM)
Efficient Planarity Testing

Journal of the ACM (JACM)
A Randomized Fully Polynomial Time Approximation Scheme for the All-Terminal Network Reliability Problem

SIAM Journal on Computing
Algorithm Design

Algorithm Design
Graph Cuts and Efficient N-D Image Segmentation

International Journal of Computer Vision
An O(n log n) algorithm for maximum st-flow in a directed planar graph

Journal of the ACM (JACM)

Counting and sampling minimum cuts in genus g graphs

Proceedings of the twenty-ninth annual symposium on Computational geometry

Quantified Score

Hi-index	5.23

Visualization

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 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.