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Approximation and hardness results for label cut and related problems

Author

Listed:
  • Peng Zhang

    (Shandong University)

  • Jin-Yi Cai

    (University of Wisconsin)

  • Lin-Qing Tang

    (Chinese Academy of Sciences
    Graduate University of Chinese Academy of Sciences)

  • Wen-Bo Zhao

    (University of California)

Abstract

We investigate a natural combinatorial optimization problem called the Label Cut problem. Given an input graph G with a source s and a sink t, the edges of G are classified into different categories, represented by a set of labels. The labels may also have weights. We want to pick a subset of labels of minimum cardinality (or minimum total weight), such that the removal of all edges with these labels disconnects s and t. We give the first non-trivial approximation and hardness results for the Label Cut problem. Firstly, we present an $O(\sqrt{m})$ -approximation algorithm for the Label Cut problem, where m is the number of edges in the input graph. Secondly, we show that it is NP-hard to approximate Label Cut within $2^{\log ^{1-1/\log\log^{c}n}n}$ for any constant c

Suggested Citation

  • Peng Zhang & Jin-Yi Cai & Lin-Qing Tang & Wen-Bo Zhao, 2011. "Approximation and hardness results for label cut and related problems," Journal of Combinatorial Optimization, Springer, vol. 21(2), pages 192-208, February.
    • Handle: RePEc:spr:jcomop:v:21:y:2011:i:2:d:10.1007_s10878-009-9222-0
    DOI: 10.1007/s10878-009-9222-0
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    References listed on IDEAS

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    1. Refael Hassin & Jérôme Monnot & Danny Segev, 2007. "Approximation algorithms and hardness results for labeled connectivity problems," Journal of Combinatorial Optimization, Springer, vol. 14(4), pages 437-453, November.
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    Cited by:

    1. Tlilane, Lydia, 2014. "Les matroïdes et leur implication dans l'allocation de ressources indivisibles : algorithmes d'approximation avec garantie de performance," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14807 edited by Monnot, Jérôme.
    2. Xianmin Liu & Jianzhong Li, 2015. "Algorithms and complexity results for labeled correlation clustering problem," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 488-501, February.
    3. Zishen Yang & Wei Wang & Majun Shi, 2021. "Algorithms and Complexity for a Class of Combinatorial Optimization Problems with Labelling," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 673-695, March.

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