Hardness of embedding metric spaces of equal size

Subhash Khot, Rishi Sake

Research output: Chapter in Book/Report/Conference proceedingConference 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(npoly(log n))). We give a simple reduction from the METRIC LABELING problem which was shown to be inapproximable by Chuzhoy and Naor [10].

Original languageEnglish (US)
Title of host publicationApproximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings
Pages218-227
Number of pages10
Volume4627 LNCS
StatePublished - 2007
Event10th 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 2007Aug 22 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4627 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007
CountryUnited States
CityPrinceton, NJ
Period8/20/078/22/07

Fingerprint

Hardness
Metric space
Embedding Problem
Polynomial-time Algorithm
Polynomials

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Computer Science(all)
  • Theoretical Computer Science

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 (Vol. 4627 LNCS, pp. 218-227). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4627 LNCS).

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. Vol. 4627 LNCS 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 proceedingConference 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. vol. 4627 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4627 LNCS, 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.
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. Vol. 4627 LNCS. 2007. p. 218-227. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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. Vol. 4627 LNCS 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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