Inapproximability of survivable networks

Yuval Lando; Zeev Nutov

doi:10.1007/978-3-540-85363-3_12

Inapproximability of survivable networks

Yuval Lando, Zeev Nutov

Computer Science discipline

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

Abstract

In the Survivable Network Design Problem (SNDP) one seeks to find a minimum cost subgraph that satisfies prescribed node-connectivity requirements. We give a novel approximation ratio preserving reduction from Directed SNDP to Undirected SNDP. Our reduction extends and widely generalizes as well as significantly simplifies the main results of [6]. Using it, we derive some new hardness of approximation results, as follows. We show that directed and undirected variants of SNDP and of k -Connected Subgraph are equivalent w.r.t. approximation, and that a ρ-approximation for Undirected Rooted SNDP implies a ρ-approximation for Directed Steiner Tree.

Original language	English
Title of host publication	Approximation, Randomization and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings
Publisher	Springer Verlag
Pages	146-152
Number of pages	7
ISBN (Print)	3540853626, 9783540853626
DOIs	https://doi.org/10.1007/978-3-540-85363-3_12
State	Published - 2008
Event	11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008 - Boston, MA, United States Duration: 25 Aug 2008 → 27 Aug 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5171 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008
Country/Territory	United States
City	Boston, MA
Period	25/08/08 → 27/08/08

Bibliographical note

Funding Information:
This research was supported by The Open University of Israel’s Research Fund (grant no. 100685). Preliminary version in APPROX, LNCS 5171, pages 146–152. Tel.: +972 9 778 1254; fax: +972 9 778 2605. E-mail addresses: [email protected] (Y. Lando), [email protected] (Z. Nutov).

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10.1007/978-3-540-85363-3_12

Cite this

Lando, Y., & Nutov, Z. (2008). Inapproximability of survivable networks. In Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings (pp. 146-152). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5171 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-85363-3_12

Lando, Yuval ; Nutov, Zeev. / Inapproximability of survivable networks. Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings. Springer Verlag, 2008. pp. 146-152 (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) one seeks to find a minimum cost subgraph that satisfies prescribed node-connectivity requirements. We give a novel approximation ratio preserving reduction from Directed SNDP to Undirected SNDP. Our reduction extends and widely generalizes as well as significantly simplifies the main results of [6]. Using it, we derive some new hardness of approximation results, as follows. We show that directed and undirected variants of SNDP and of k -Connected Subgraph are equivalent w.r.t. approximation, and that a ρ-approximation for Undirected Rooted SNDP implies a ρ-approximation for Directed Steiner Tree.",

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Lando, Y & Nutov, Z 2008, Inapproximability of survivable networks. in Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5171 LNCS, Springer Verlag, pp. 146-152, 11th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2008 and 12th International Workshop on Randomization and Computation, RANDOM 2008, Boston, MA, United States, 25/08/08. https://doi.org/10.1007/978-3-540-85363-3_12

Inapproximability of survivable networks. / Lando, Yuval; Nutov, Zeev.
Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings. Springer Verlag, 2008. p. 146-152 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5171 LNCS).

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

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Lando Y, Nutov Z. Inapproximability of survivable networks. In Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques - 11th International Workshop, APPROX 2008 and 12th International Workshop, RANDOM 2008, Proceedings. Springer Verlag. 2008. p. 146-152. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-85363-3_12

Inapproximability of survivable networks

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