Hardness of approximation for vertex-connectivity network-design problems

Guy Kortsarz; Robert Krauthgamer; James R. Lee

doi:10.1007/3-540-45753-4_17

Hardness of approximation for vertex-connectivity network-design problems

Guy Kortsarz, Robert Krauthgamer, James R. Lee

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In the survivable network design problem SNDP, the goal is to find a minimum-cost subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertex-disjoint paths connecting them. We give the first lower bound on the approximability of SNDP, showing that the problem admits no efficient (formula presented) ratio approximation for any fixed ε > 0 unless NP ⊆ DTIME(n^polylog(ⁿ⁾). We also show hardness of approximation results for several important special cases of SNDP, including constant factor hardness for the k-vertex connected spanning subgraph problem (k-VCSS) and for the vertex-connectivity augmentation problem, even when the edge costs are severely restricted.

Original language	English
Title of host publication	Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings
Editors	Klaus Jansen, Stefano Leonardi, Vijay Vazirani
Publisher	Springer Verlag
Pages	185-199
Number of pages	15
ISBN (Print)	3540441867, 9783540441861
DOIs	https://doi.org/10.1007/3-540-45753-4_17
State	Published - 2002
Externally published	Yes
Event	5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002 - Rome, Italy Duration: 17 Sep 2002 → 21 Sep 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2462
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002
Country/Territory	Italy
City	Rome
Period	17/09/02 → 21/09/02

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

Access to Document

10.1007/3-540-45753-4_17

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Kortsarz, G., Krauthgamer, R., & Lee, J. R. (2002). Hardness of approximation for vertex-connectivity network-design problems. In K. Jansen, S. Leonardi, & V. Vazirani (Eds.), Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings (pp. 185-199). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2462). Springer Verlag. https://doi.org/10.1007/3-540-45753-4_17

Kortsarz, Guy ; Krauthgamer, Robert ; Lee, James R. / Hardness of approximation for vertex-connectivity network-design problems. Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings. editor / Klaus Jansen ; Stefano Leonardi ; Vijay Vazirani. Springer Verlag, 2002. pp. 185-199 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In the survivable network design problem SNDP, the goal is to find a minimum-cost subgraph satisfying certain connectivity requirements. We study the vertex-connectivity variant of SNDP in which the input specifies, for each pair of vertices, a required number of vertex-disjoint paths connecting them. We give the first lower bound on the approximability of SNDP, showing that the problem admits no efficient (formula presented) ratio approximation for any fixed ε > 0 unless NP ⊆ DTIME(npolylog(n)). We also show hardness of approximation results for several important special cases of SNDP, including constant factor hardness for the k-vertex connected spanning subgraph problem (k-VCSS) and for the vertex-connectivity augmentation problem, even when the edge costs are severely restricted.",

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Kortsarz, G, Krauthgamer, R & Lee, JR 2002, Hardness of approximation for vertex-connectivity network-design problems. in K Jansen, S Leonardi & V Vazirani (eds), Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2462, Springer Verlag, pp. 185-199, 5th International Workshop On Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002, Rome, Italy, 17/09/02. https://doi.org/10.1007/3-540-45753-4_17

Hardness of approximation for vertex-connectivity network-design problems. / Kortsarz, Guy; Krauthgamer, Robert; Lee, James R.
Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings. ed. / Klaus Jansen; Stefano Leonardi; Vijay Vazirani. Springer Verlag, 2002. p. 185-199 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2462).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Kortsarz G, Krauthgamer R, Lee JR. Hardness of approximation for vertex-connectivity network-design problems. In Jansen K, Leonardi S, Vazirani V, editors, Approximation Algorithms for Combinatorial Optimization - 5th International Workshop, APPROX 2002, Proceedings. Springer Verlag. 2002. p. 185-199. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-45753-4_17

Hardness of approximation for vertex-connectivity network-design problems

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