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\u00f0log n\u00de: This improves upon the result of Bartal who gave a bound of O\u00f0log n loglog n\u00de: Moreover, our result is existentially tight; there exist metric spaces where any tree embedding must have distortion O\u00f0log n\u00de-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.<\/p>\n","protected":false},"excerpt":{"rendered":"
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\u00f0log n\u00de: This improves upon the result of Bartal who gave a bound of O\u00f0log n loglog n\u00de: Moreover, our result is existentially tight; there […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Elsevier","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"3","msr_journal":"Journal of Computer and System 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