Hardness of Embedding Metric Spaces of Equal Size

Authors:
Subhash Khot;Rishi Saket
Affiliations:
Georgia Institute of Technology,;Georgia Institute of Technology,
Venue:
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Year:
2007

Citing 14
Cited 1

Probabilistic checking of proofs: a new characterization of NP

Journal of the ACM (JACM)
On approximating arbitrary metrices by tree metrics

STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems

Journal of the ACM (JACM)
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems

Journal of the ACM (JACM)
Approximation algorithms for the metric labeling problem via a new linear programming formulation

SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms for classification problems with pairwise relationships: metric labeling and Markov random fields

Journal of the ACM (JACM)
Algorithmic Applications of Low-Distortion Geometric Embeddings

FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Expander flows, geometric embeddings and graph partitioning

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Low distortion maps between point sets

STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Hardness of Metric Labeling

FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics

Journal of Computer and System Sciences - Special issue: STOC 2003
Low-distortion embeddings of general metrics into the line

Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Euclidean distortion and the sparsest cut

Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The complexity of low-distortion embeddings between point sets

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms

Inapproximability for planar embedding problems

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms

Quantified Score

Hi-index	0.00

Visualization

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 茂戮驴((logn)1/4 茂戮驴茂戮驴) for any constant 茂戮驴 0, unless $\textnormal{NP} \subseteq \textnormal{DTIME}(n^{\textnormal{poly}(\log n))})$. We give a simple reduction from the METRIC LABELINGproblem which was shown to be inapproximable by Chuzhoy and Naor [10].