A tight bound on approximating arbitrary metrics by tree metrics
- Jittat Fakcharoenphol ,
- Satish Rao ,
- Kunal Talwar
STOC '03: Proceedings of the thirty-fifth annual ACM symposium on Theory of computing |
Published by Association for Computing Machinery, Inc.
In this paper, we show that any n point metric space can be embedded into a distribution over dominating tree metrics such that the expected stretch of any edge is Oðlog nÞ: This improves upon the result of Bartal who gave a bound of Oðlog n loglog nÞ: Moreover, our result is existentially tight; there exist metric spaces where any tree embedding must have distortion Oðlog nÞ-distortion. This problem lies at the heart of numerous approximation and online algorithms including ones for group Steiner tree, metric labeling, buy-at-bulk network design and metrical task system. Our result improves the performance guarantees for all of these problems.
Copyright © 2007 by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Publications Dept, ACM Inc., fax +1 (212) 869-0481, or permissions@acm.org. The definitive version of this paper can be found at ACM's Digital Library --http://www.acm.org/dl/.