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Probabilistic Approximation of Metric Spaces and its Algorithmic Applications (1996)
| Venue: | In 37th Annual Symposium on Foundations of Computer Science |
| Citations: | 351 - 32 self |
BibTeX
@INPROCEEDINGS{Bartal96probabilisticapproximation,
author = {Yair Bartal},
title = {Probabilistic Approximation of Metric Spaces and its Algorithmic Applications},
booktitle = {In 37th Annual Symposium on Foundations of Computer Science},
year = {1996},
pages = {184--193}
}
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Abstract
The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to low-distortion embeddings in low-dimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized algorithms for optimization problems on metric spaces, by relating the randomized performance ratio for any metric space to the randomized performance ratio for a set of "simple" metric spaces. We define a notion of a set of metric spaces that probabilistically-approximates another metric space. We prove that any metric space can be probabilistically-approximated by hierarchically well-separated trees (HST) with a polylogarithmic distortion. These metric spaces are "simple" as being: (1) tree metrics. (2) natural for applying a divide-and-conquer algorithmic approach. The technique presented is of particular interest in the context of on-line computation. A large number of on-line al...
Keyphrases
metric space algorithmic application probabilistic approximation simple metric space many algorithmic application low-dimensional space particular interest divide-and-conquer algorithmic approach randomized algorithm on-line al performance ratio optimization problem novel technique large number polylogarithmic distortion randomized performance ratio low-distortion embeddings tree metric on-line computation graph spanner well-separated tree
