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Generalizedk-multiway cut problems

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Abstract

This paper considers the following problem: given an edgeweighted graphG = (V, E, w) and disjointk-subsetsU p ofV, find a minimum weighted set of edgesE′ ⊆E such that its removal disconnects the graph intok parts and each part contains exactly one vertex from eachU p for 1 ≤p ≤r. This generalizes some well-known NP-hard problems. In this paper, we first apply greedy local search algorithm to obtain better approximation solutions. Then we give a randomized local search algorithm which produces a solution within a factor (1 + ε) with the probability at least (1 - 1/e) for any small ε. Simple near-optimum approximation algorithms are also proposed.

Analogously, there is a maximumk-multiway cut problem with the same restrictions.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Lethbridge, T1K 3M4, Lethbridge, Alberta, Canada

    Jiping Liu

  2. Department of Mathematics and Computer Science, Indiana State University, 47809, Terre Haute, IN, USA

    Yuejian Peng & Cheng Zhao

Authors
  1. Jiping Liu
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  2. Yuejian Peng
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  3. Cheng Zhao
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Correspondence to Cheng Zhao.

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Liu, J., Peng, Y. & Zhao, C. Generalizedk-multiway cut problems. J. Appl. Math. Comput. 21, 69–82 (2006). https://doi.org/10.1007/BF02896389

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  • DOI: https://doi.org/10.1007/BF02896389

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