## Probabilistic Approximation of Metric Spaces and its Algorithmic Applications (1996)

Venue: | In 37th Annual Symposium on Foundations of Computer Science |

Citations: | 314 - 29 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}

}

### Years of Citing Articles

### OpenURL

### 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...