On the complexity of the multicut problem in bounded tree-width graphs and digraphs

Authors:
Cédric Bentz
Affiliations:
LRI, University of Paris-Sud and CNRS, Orsay F-91405, France
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 12
Cited 5

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Directed tree-width

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Approximate Max-Flow Min-(Multi)Cut Theorems and Their Applications

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Improved results for directed multicut

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Complexity and exact algorithms for multicut

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Note: A simple algorithm for multicuts in planar graphs with outer terminals

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An approximation algorithm for the Generalized k-Multicut problem

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CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
A polynomial-time algorithm for planar multicuts with few source-sink pairs

IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation

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Abstract

Given an edge- or vertex-weighted graph or digraph and a list of source-sink pairs, the minimum multicut problem consists in selecting a minimum weight set of edges or vertices whose removal leaves no path from each source to the corresponding sink. This is a classical NP-hard problem, and we show that the edge version becomes tractable in bounded tree-width graphs if the number of source-sink pairs is fixed, but remains NP-hard in directed acyclic graphs and APX-hard in bounded tree-width and bounded degree unweighted digraphs. The vertex version, although tractable in trees, is proved to be NP-hard in unweighted cacti of bounded degree and bounded path-width.