Probabilistic approximation of metric spaces and its algorithmic applications
- International Computer Science Institute, Berkeley, CA (United States)
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 an, metric space to the randomized performance ratio for a set of {open_quotes}simple{close_quotes} metric spaces. We define a notion of a set of metric spaces that probabilistically-approximates another metric space. We prove that an, metric space can be probabilistically- approximated by hierarchically well-separated trees (HST) with a polylogarithmic distortion. These metric spaces are {open_quotes}simple{close_quotes} 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 algorithmic problems, including metrical task systems [BLS87], server problems [MMS88], distributed paging [BFR92], and dynamic storage rearrangement [FMRW95], are defined in terms of some metric space. Typically for these problems, there are linear lower bounds on the competitive ratio of deterministic algorithms. Although randomization against an oblivious adversary has the potential of overcoming these high ratios, very little progress has been made in the analysis. We demonstrate the use of our technique by obtaining substantially improved results for two different on-line problems. For metrical task systems [BLS87] we give first sub-linear randomized competitive ratio for a large set of metric spaces. For constrained file migration [BFR92] we give first randomized algorithms for general networks with polylogarithmic competitive ratio.
- OSTI ID:
- 457650
- Report Number(s):
- CONF-961004-; TRN: 97:001036-0021
- Resource Relation:
- Conference: 37. annual symposium on foundations of computer science, Burlington, VT (United States), 13-16 Oct 1996; Other Information: PBD: 1996; Related Information: Is Part Of Proceedings of the 37th annual symposium on foundations of computer science; PB: 656 p.
- Country of Publication:
- United States
- Language:
- English
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