Journal of Combinatorial Optimization

, Volume 20, Issue 3, pp 249–258 | Cite as

Hardness of k-Vertex-Connected Subgraph Augmentation Problem

  • Changcun Ma
  • Donghyun Kim
  • Yuexuan Wang
  • Wei Wang
  • Nassim Sohaee
  • Weili Wu
Article

Abstract

Given a k-connected graph G=(V,E) and VV, k-Vertex-Connected Subgraph Augmentation Problem (k-VCSAP) is to find SVV with minimum cardinality such that the subgraph induced by VS 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 NPDTIME(nO(log log n)), where n is the size of an input graph.

Keywords

Network survivability Graph connectivity 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Changcun Ma
    • 1
  • Donghyun Kim
    • 2
  • Yuexuan Wang
    • 1
  • Wei Wang
    • 3
  • Nassim Sohaee
    • 2
  • Weili Wu
    • 2
  1. 1.Institute for Theoretical Computer ScienceTsinghua UniversityBeijingPeople’s Republic of China
  2. 2.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA
  3. 3.Department of MathematicsXi’an Jiaotong UniversityXi’anPeople’s Republic of China

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