A Tight Bound on Approximating Arbitrary Metrics by Tree Metrics

A Tight Bound on Approximating Arbitrary Metrics by Tree Metrics (2003)

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by Jittat Fakcharoenphol , Satish Rao , Kunal Talwar

Venue:	In Proceedings of the 35th Annual ACM Symposium on Theory of Computing
Citations:	216 - 3 self

BibTeX

@INPROCEEDINGS{Fakcharoenphol03atight,
    author = {Jittat Fakcharoenphol and Satish Rao and Kunal Talwar},
    title = {A Tight Bound on Approximating Arbitrary Metrics by Tree Metrics},
    booktitle = {In Proceedings of the 35th Annual ACM Symposium on Theory of Computing},
    year = {2003},
    pages = {448--455}
}

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Abstract

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 O(log n). This improves upon the result of Bartal who gave a bound of O(log n log log n). Moreover, our result is existentially tight; there exist metric spaces where any tree embedding must have distortion#sto n)-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.

Citations

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