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Probabilistic Approximation of Metric Spaces and its Algorithmic Applications
 In 37th Annual Symposium on Foundations of Computer Science
, 1996
"... The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional spaces [LLR94], having many algorithmic applications. This paper provides a novel technique for the analysis of randomized ..."
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Cited by 323 (28 self)
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The goal of approximating metric spaces by more simple metric spaces has led to the notion of graph spanners [PU89, PS89] and to lowdistortion embeddings in lowdimensional 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 probabilisticallyapproximates another metric space. We prove that any metric space can be probabilisticallyapproximated by hierarchically wellseparated trees (HST) with a polylogarithmic distortion. These metric spaces are "simple" as being: (1) tree metrics. (2) natural for applying a divideandconquer algorithmic approach. The technique presented is of particular interest in the context of online computation. A large number of online al...
On Approximating Arbitrary Metrics by Tree Metrics
 In Proceedings of the 30th Annual ACM Symposium on Theory of Computing
, 1998
"... This paper is concerned with probabilistic approximation of metric spaces. In previous work we introduced the method of ecient approximation of metrics by more simple families of metrics in a probabilistic fashion. In particular we study probabilistic approximations of arbitrary metric spaces by \hi ..."
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Cited by 260 (13 self)
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This paper is concerned with probabilistic approximation of metric spaces. In previous work we introduced the method of ecient approximation of metrics by more simple families of metrics in a probabilistic fashion. In particular we study probabilistic approximations of arbitrary metric spaces by \hierarchically wellseparated tree" metric spaces. This has proved as a useful technique for simplifying the solutions to various problems.
Competitive Algorithms for Distributed Data Management
 In Proceedings of the 24th Annual ACM Symposium on Theory of Computing
"... We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem ([DF], [ML]), where copies of a file may be be stored in the local storage of some subset of processors. Copies may be replicated and discarded over time so ..."
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Cited by 100 (8 self)
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We deal with the competitive analysis of algorithms for managing data in a distributed environment. We deal with the file allocation problem ([DF], [ML]), where copies of a file may be be stored in the local storage of some subset of processors. Copies may be replicated and discarded over time so as to optimize communication costs, but multiple copies must be kept consistent and at least one copy must be stored somewhere in the network at all times. We deal with competitive algorithms for minimizing communication costs, over arbitrary sequences of reads and writes, and arbitrary network topologies. We define the constrained file allocation problem to be the solution of many individual file allocation problems simultaneously, subject to the constraints of local memory size. We give competitive algorithms for this problem on the uniform network topology. We then introduce distributed competitive algorithms for online data tracking (a generalization of mobile user tracking [AP1...
On Page Migration and Other Relaxed Task Systems
, 1997
"... This paper is concerned with the page migration (or file migration) problem [BS89] as part of a large class of online problems. The page migration problem deals with the management of pages residing in a network of processors. In the classical problem there is only one copy of each page which is ..."
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Cited by 28 (4 self)
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This paper is concerned with the page migration (or file migration) problem [BS89] as part of a large class of online problems. The page migration problem deals with the management of pages residing in a network of processors. In the classical problem there is only one copy of each page which is accessed by different processors over time. The page is allowed to be migrated between processors. However a migration incurs higher communication cost than an access (proportionally to the page size). The problem is that of deciding when and where to migrate the page in order to lower access costs. A more general setting is the kpage migration where we wish to maintain k copies of the page. The page migration problems are concerned with a dilemma common to many online problems: determining when is it beneficial to make configuration changes. We deal with the relaxed task systems model which captures a large class of problems of this type, that can be described as the generalizati...
The Distributed kServer Problem  A Competitive Distributed Translator for kServer Algorithms
, 1992
"... We consider the kserver problem [23] in a distributed setting. ..."
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Cited by 13 (3 self)
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We consider the kserver problem [23] in a distributed setting.
KServer Problem
"... pace M with a distance function d (which is symmetric in most of the cases we consider). There are k servers in this space. The request sequence is oe = oe 1 oe 2 : : :, where oe i is a point in M . The online algorithm's response to oe i should be to move a server j to point oe i to serve the reque ..."
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pace M with a distance function d (which is symmetric in most of the cases we consider). There are k servers in this space. The request sequence is oe = oe 1 oe 2 : : :, where oe i is a point in M . The online algorithm's response to oe i should be to move a server j to point oe i to serve the request. The cost measure is the total distance moved by all the servers. Example: Let M be the uniform metric space over n points. That is the metric space where the distance between every pair of points is 1. It is easy to see that the kserver problem on the uniform metric space is isomorphic to the paging problem with n pages in slow memory and a cache of size k. Each
Online Computation & Network Algorithms  Lecture 6
, 1997
"... who show that the Work Function Algorithm is 2k \Gamma 1competitive. 6.1.1 The 2Server Problem There are several known algorithms that achieve an optimal competitive ratio of 2 for the 2server problem. We will present here a simple approach due to Chrobak and Larmore [CL90]. There are a couple ..."
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who show that the Work Function Algorithm is 2k \Gamma 1competitive. 6.1.1 The 2Server Problem There are several known algorithms that achieve an optimal competitive ratio of 2 for the 2server problem. We will present here a simple approach due to Chrobak and Larmore [CL90]. There are a couple of ideas that enable us to give a 2competitive algorithm that works for any metric space. 61 62 Lecture 6: February 6 The first is that "adding points to a metric space often makes it easier to work in and reason about them". It must be noted that these imaginary points are not there in the metric space, and so the servers cannot move to those points, but must keep it in memory and perform further calculations as if they are really at that point. s(x, y, z) s(z, x, y) x f y z y z x s(y, x, z) The second is the following construction. Suppose we have 3 po