Hardness of k-Vertex-Connected Subgraph Augmentation Problem

Changcun Ma (), Donghyun Kim (), Yuexuan Wang (), Wei Wang (), Nassim Sohaee () and Weili Wu ()
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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

Journal of Combinatorial Optimization, 2010, vol. 20, issue 3, No 3, 249-258

Abstract: 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.

Keywords: Network survivability; Graph connectivity (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-008-9206-5

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