Hardness of k-Vertex-Connected Subgraph Augmentation Problem

Authors:
Changcun Ma;Donghyun Kim;Yuexuan Wang;Wei Wang;Nassim Sohaee;Weili Wu
Affiliations:
Institute for Theoretical Computer Science, Tsinghua University, Beijing, People's Republic of China 100084;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75083;Institute for Theoretical Computer Science, Tsinghua University, Beijing, People's Republic of China 100084;Department of Mathematics, Xi'an Jiaotong University, Xi'an, People's Republic of China 710049;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75083;Department of Computer Science, University of Texas at Dallas, Richardson, USA 75083
Venue:
Journal of Combinatorial Optimization
Year:
2010

Citing 8
Cited 0

Maximum bounded 3-dimensional matching is MAX SNP-complete

Information Processing Letters
A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP

STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
A note on the vertex-connectivity augmentation problem

Journal of Combinatorial Theory Series B
Approximating the Domatic Number

SIAM Journal on Computing
Approximation algorithms for combinatorial problems

STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Hardness of Approximation for Vertex-Connectivity Network Design Problems

SIAM Journal on Computing
Survivable network design with degree or order constraints

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A survey on sensor networks

IEEE Communications Magazine

Quantified Score

Hi-index	0.01

Visualization

Abstract

Given a k-connected graph G=(V,E) and V 驴驴V, k-Vertex-Connected Subgraph Augmentation Problem (k-VCSAP) is to find S驴V驴V 驴 with minimum cardinality such that the subgraph induced by V 驴驴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驴(log驴n)) unless P=NP and O(log驴n) unless NP驴DTIME(n O(log驴log驴n)), where n is the size of an input graph.