Computing finest mincut partitions of a graph and application to routing problems

Authors:
Gerhard Reinelt;Dirk Oliver Theis;Klaus Michael Wenger
Affiliations:
University of Heidelberg, Institute of Computer Science, Discrete Optimization Research Group, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany;University of Heidelberg, Institute of Computer Science, Discrete Optimization Research Group, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany;University of Heidelberg, Institute of Computer Science, Discrete Optimization Research Group, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

Let G=(V,E,w) be an n-vertex graph with edge weights w0. We propose an algorithm computing all partitions of V into mincuts of G such that the mincuts in the partitions cannot be partitioned further into mincuts. There are O(n) such finest mincut partitions. A mincut is a non-empty proper subset of V such that the total weight of edges with exactly one end in the subset is minimal. The proposed algorithm exploits the cactus representation of mincuts and has the same time complexity as cactus construction. An application to the exact solution of the general routing problem is described.