A (1 + ln 2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius

Nachshon Cohen; Zeev Nutov

doi:10.1007/978-3-642-22935-0_13

A (1 + ln 2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius

Nachshon Cohen, Zeev Nutov

Open University of Israel

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

Abstract

We consider the Tree Augmentation problem: given a graph G = (V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F ⊆ E such that T ∪ F is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimum-cost edge-cover F ⊆ E of a laminar set-family. The best known approximation ratio for Tree Augmentation is 2, even for trees of radius 2. As laminar families play an important role in network design problems, obtaining a better ratio is a major open problem in network design. We give a (1 + ln 2)-approximation algorithm for trees of constant radius. Our algorithm is based on a new decomposition of problem solutions, which may be of independent interest.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings
Pages	147-157
Number of pages	11
DOIs	https://doi.org/10.1007/978-3-642-22935-0_13
State	Published - 2011
Event	14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011 - Princeton, NJ, United States Duration: 17 Aug 2011 → 19 Aug 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6845 LNCS

Conference

Conference	14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011
Country/Territory	United States
City	Princeton, NJ
Period	17/08/11 → 19/08/11

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-22935-0_13

Cite this

Cohen, N., & Nutov, Z. (2011). A (1 + ln 2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings (pp. 147-157). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6845 LNCS). https://doi.org/10.1007/978-3-642-22935-0_13

Cohen, Nachshon ; Nutov, Zeev. / A (1 + ln 2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings. 2011. pp. 147-157 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We consider the Tree Augmentation problem: given a graph G = (V,E) with edge-costs and a tree T on V disjoint to E, find a minimum-cost edge-subset F ⊆ E such that T ∪ F is 2-edge-connected. Tree Augmentation is equivalent to the problem of finding a minimum-cost edge-cover F ⊆ E of a laminar set-family. The best known approximation ratio for Tree Augmentation is 2, even for trees of radius 2. As laminar families play an important role in network design problems, obtaining a better ratio is a major open problem in network design. We give a (1 + ln 2)-approximation algorithm for trees of constant radius. Our algorithm is based on a new decomposition of problem solutions, which may be of independent interest.",

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Cohen, N & Nutov, Z 2011, A (1 + ln 2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6845 LNCS, pp. 147-157, 14th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2011 and the 15th International Workshop on Randomization and Computation, RANDOM 2011, Princeton, NJ, United States, 17/08/11. https://doi.org/10.1007/978-3-642-22935-0_13

A (1 + ln 2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius. / Cohen, Nachshon; Nutov, Zeev.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings. 2011. p. 147-157 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6845 LNCS).

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

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Cohen N, Nutov Z. A (1 + ln 2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 14th International Workshop, APPROX 2011 and 15th International Workshop, RANDOM 2011, Proceedings. 2011. p. 147-157. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-22935-0_13

A (1 + ln 2)-approximation algorithm for minimum-cost 2-edge-connectivity augmentation of trees with constant radius

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