Hardness of embedding metric spaces of equal size

Subhash Khot; Rishi Sake

doi:10.1007/978-3-540-74208-1_16

Hardness of embedding metric spaces of equal size

Subhash Khot, Rishi Sake

Computer Science

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

Abstract

We study the problem embedding an n-point metric space into another n-point metric space while minimizing distortion. We show that there is no polynomial time algorithm to approximate the minimum distortion within a factor of Ω((log n)^1/4-δ) for any constant δ > 0, unless NP ⊆ DTIME(n^{poly(log n))}). We give a simple reduction from the METRIC LABELING problem which was shown to be inapproximable by Chuzhoy and Naor [10].

Original language	English (US)
Title of host publication	Approximation, Randomization, and Combinatorial Optimization
Subtitle of host publication	Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings
Publisher	Springer Verlag
Pages	218-227
Number of pages	10
ISBN (Print)	9783540742074
DOIs	https://doi.org/10.1007/978-3-540-74208-1_16
State	Published - 2007
Event	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 - Princeton, NJ, United States Duration: Aug 20 2007 → Aug 22 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4627 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
Country/Territory	United States
City	Princeton, NJ
Period	8/20/07 → 8/22/07

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-540-74208-1_16

Cite this

Khot, S., & Sake, R. (2007). Hardness of embedding metric spaces of equal size. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings (pp. 218-227). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-74208-1_16

Hardness of embedding metric spaces of equal size. / Khot, Subhash; Sake, Rishi.
Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag, 2007. p. 218-227 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS).

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

Khot, S & Sake, R 2007, Hardness of embedding metric spaces of equal size. in Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4627 LNCS, Springer Verlag, pp. 218-227, 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007, Princeton, NJ, United States, 8/20/07. https://doi.org/10.1007/978-3-540-74208-1_16

Khot S, Sake R. Hardness of embedding metric spaces of equal size. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag. 2007. p. 218-227. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-74208-1_16

Khot, Subhash ; Sake, Rishi. / Hardness of embedding metric spaces of equal size. Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings. Springer Verlag, 2007. pp. 218-227 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Hardness of embedding metric spaces of equal size

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