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Hardness of k-Vertex-Connected Subgraph Augmentation Problem

Author

Listed:
  • Changcun Ma

    (Tsinghua University)

  • Donghyun Kim

    (University of Texas at Dallas)

  • Yuexuan Wang

    (Tsinghua University)

  • Wei Wang

    (Xi’an Jiaotong University)

  • Nassim Sohaee

    (University of Texas at Dallas)

  • Weili Wu

    (University of Texas at Dallas)

Abstract

Given a k-connected graph G=(V,E) and V ′⊂V, k-Vertex-Connected Subgraph Augmentation Problem (k-VCSAP) is to find S⊂V∖V ′ with minimum cardinality such that the subgraph induced by V ′∪S is k-connected. In this paper, we study the hardness of k-VCSAP in undirect graphs. We first prove k-VCSAP is APX-hard. Then, we improve the lower bound in two ways by relying on different assumptions. That is, we prove no algorithm for k-VCSAP has a PR better than O(log (log n)) unless P=NP and O(log n) unless NP⊆DTIME(n O(log log n)), where n is the size of an input graph.

Suggested Citation

  • Changcun Ma & Donghyun Kim & Yuexuan Wang & Wei Wang & Nassim Sohaee & Weili Wu, 2010. "Hardness of k-Vertex-Connected Subgraph Augmentation Problem," Journal of Combinatorial Optimization, Springer, vol. 20(3), pages 249-258, October.
    • Handle: RePEc:spr:jcomop:v:20:y:2010:i:3:d:10.1007_s10878-008-9206-5
    DOI: 10.1007/s10878-008-9206-5
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    Cited by:

    1. Chitra Balasubramaniam & Sergiy Butenko, 2017. "On robust clusters of minimum cardinality in networks," Annals of Operations Research, Springer, vol. 249(1), pages 17-37, February.

    More about this item

    Keywords

    Network survivability; Graph connectivity;

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