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2003
ACM

A tight bound on approximating arbitrary metrics by tree metrics

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A tight bound on approximating arbitrary metrics by tree metrics
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 (log 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. Categories and Subject Descriptors G.2.2 [Discrete Mathematics]: Graph Theory--Graph Algorithms General Terms Algorithms, Theory Keywords Metrics, Embeddings, Tree metrics
Jittat Fakcharoenphol, Satish Rao, Kunal Talwar
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2003
Where STOC
Authors Jittat Fakcharoenphol, Satish Rao, Kunal Talwar
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