### 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) |
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Title of host publication | Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings |

Pages | 218-227 |

Number of pages | 10 |

Volume | 4627 LNCS |

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) |
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Volume | 4627 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and 11th International Workshop on Randomization and Computation, RANDOM 2007 |
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Country | United States |

City | Princeton, NJ |

Period | 8/20/07 → 8/22/07 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

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

*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.

}

TY - GEN

T1 - Hardness of embedding metric spaces of equal size

AU - Khot, Subhash

AU - Sake, Rishi

PY - 2007

Y1 - 2007

N2 - 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].

AB - 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].

UR - http://www.scopus.com/inward/record.url?scp=38049011004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38049011004&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:38049011004

SN - 9783540742074

VL - 4627 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 218

EP - 227

BT - Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 10th International Workshop, APPROX 2007 and 11th International Workshop, RANDOM 2007, Proceedings

ER -