A tight bound on approximating arbitrary metrics by tree metrics

Jittat Fakcharoenphol, Satish Rao, Kunal Talwar
2004 Journal of computer and system sciences (Print)  
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 log log 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
more » ... ner tree, metric labeling, buy-at-bulk network design and metrical task system. Our result improves the performance guarantees for all of these problems. r
doi:10.1016/j.jcss.2004.04.011 fatcat:6blzko5t4fhifbqs2v4jtxkp7e