Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs

Victor Chepoi; Feodor F. Dragan; Ilan Newman; Yuri Rabinovich; Yann Vaxès

doi:10.1007/978-3-642-15369-3_8

Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs

Victor Chepoi, Feodor F. Dragan, Ilan Newman, Yuri Rabinovich, Yann Vaxès

Department of Computer Science

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

Abstract

We present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding (unweighted) graph metrics into tree metrics (thus improving and simplifying the factor 100 and 27 algorithms of Bǎdoiu et al. (2007) and Bǎdoiu et al. (2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding graph metrics into outerplanar metrics. For this, we introduce a notion of metric relaxed minor and show that if G contains an α-metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is ≥ α. Then, for H = K_2,3, we present an algorithm which either finds an α-relaxed minor, or produces an O(α)-embedding into an outerplanar metric.

Original language	English
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings
Pages	95-109
Number of pages	15
DOIs	https://doi.org/10.1007/978-3-642-15369-3_8
State	Published - 2010
Event	13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010 - Barcelona, Spain Duration: 1 Sep 2010 → 3 Sep 2010

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6302 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010
Country/Territory	Spain
City	Barcelona
Period	1/09/10 → 3/09/10

Bibliographical note

Funding Information:
This research was partly supported by the ANR grant BLANC GGAA.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/978-3-642-15369-3_8

Cite this

Chepoi, V., Dragan, F. F., Newman, I., Rabinovich, Y., & Vaxès, Y. (2010). Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings (pp. 95-109). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6302 LNCS). https://doi.org/10.1007/978-3-642-15369-3_8

Chepoi, Victor ; Dragan, Feodor F. ; Newman, Ilan et al. / Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. pp. 95-109 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs",

abstract = "We present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding (unweighted) graph metrics into tree metrics (thus improving and simplifying the factor 100 and 27 algorithms of Bǎdoiu et al. (2007) and Bǎdoiu et al. (2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding graph metrics into outerplanar metrics. For this, we introduce a notion of metric relaxed minor and show that if G contains an α-metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is ≥ α. Then, for H = K2,3, we present an algorithm which either finds an α-relaxed minor, or produces an O(α)-embedding into an outerplanar metric.",

author = "Victor Chepoi and Dragan, {Feodor F.} and Ilan Newman and Yuri Rabinovich and Yann Vax{\`e}s",

note = "Funding Information: This research was partly supported by the ANR grant BLANC GGAA.; 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010 ; Conference date: 01-09-2010 Through 03-09-2010",

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Chepoi, V, Dragan, FF, Newman, I , Rabinovich, Y & Vaxès, Y 2010, Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6302 LNCS, pp. 95-109, 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010 and 14th International Workshop on Randomization and Computation, RANDOM 2010, Barcelona, Spain, 1/09/10. https://doi.org/10.1007/978-3-642-15369-3_8

Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs. / Chepoi, Victor; Dragan, Feodor F.; Newman, Ilan et al.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. p. 95-109 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6302 LNCS).

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

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AU - Dragan, Feodor F.

AU - Newman, Ilan

AU - Rabinovich, Yuri

AU - Vaxès, Yann

N1 - Funding Information: This research was partly supported by the ANR grant BLANC GGAA.

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Y1 - 2010

N2 - We present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding (unweighted) graph metrics into tree metrics (thus improving and simplifying the factor 100 and 27 algorithms of Bǎdoiu et al. (2007) and Bǎdoiu et al. (2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding graph metrics into outerplanar metrics. For this, we introduce a notion of metric relaxed minor and show that if G contains an α-metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is ≥ α. Then, for H = K2,3, we present an algorithm which either finds an α-relaxed minor, or produces an O(α)-embedding into an outerplanar metric.

AB - We present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding (unweighted) graph metrics into tree metrics (thus improving and simplifying the factor 100 and 27 algorithms of Bǎdoiu et al. (2007) and Bǎdoiu et al. (2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding graph metrics into outerplanar metrics. For this, we introduce a notion of metric relaxed minor and show that if G contains an α-metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is ≥ α. Then, for H = K2,3, we present an algorithm which either finds an α-relaxed minor, or produces an O(α)-embedding into an outerplanar metric.

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Chepoi V, Dragan FF, Newman I , Rabinovich Y, Vaxès Y. Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. 2010. p. 95-109. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-15369-3_8

Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs

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ASJC Scopus subject areas

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