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Discrete Applied Mathematics
Volume 156, Issue 3, 1 February 2008, Pages 385-396
Combinatorial Optimization 2004, CO2004
 
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doi:10.1016/j.dam.2007.03.022    
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Copyright © 2007 Elsevier B.V. All rights reserved.

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

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Gerhard Reinelta, E-mail The Corresponding Author, Dirk Oliver Theisa, E-mail The Corresponding Author and Klaus Michael Wengera, E-mail The Corresponding Author

aUniversity of Heidelberg, Institute of Computer Science, Discrete Optimization Research Group, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany


Received 20 July 2004; 
revised 3 October 2005; 
accepted 6 March 2007. 
Available online 10 May 2007.

Abstract

Let G=(V,E,w) be an n-vertex graph with edge weights w>0. 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 View the MathML source 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.

Keywords: Minimum cut; Finest partition; Clustering; Cactus; Routing problem

Article Outline

1. Introduction and terminology
2. The cactus representation of mincuts
3. Finest mincut partitions
4. The algorithm
5. Application to routing problems
5.1. The general routing problem and its special cases
5.2. Shrinking finest mincut partitions
5.3. Computational experiences
6. Summary and conclusions
Acknowledgements
References






Discrete Applied Mathematics
Volume 156, Issue 3, 1 February 2008, Pages 385-396
Combinatorial Optimization 2004, CO2004
 
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