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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 361 (33 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 281 (16 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.
Distributed Paging for General Networks
, 1996
"... Distributed paging [BFR92, ABF93b, AK95] deals with the dynamic allocation of copies of files in a distributed network as to minimize the total communication cost over a sequence of read and write requests. Most previous work deals with the file allocation problem [BS89, West91, CLRW93, ABF93a, ..."
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Cited by 62 (5 self)
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Distributed paging [BFR92, ABF93b, AK95] deals with the dynamic allocation of copies of files in a distributed network as to minimize the total communication cost over a sequence of read and write requests. Most previous work deals with the file allocation problem [BS89, West91, CLRW93, ABF93a, WY93, Koga93, AK94, LRWY94] where infinite nodal memory capacity is assumed. In contrast the distributed paging problem makes the more realistic assumption that nodal memory capacity is limited. Former work on distributed paging deals with the problem only in the case of a uniform network topology. This paper gives the first distributed paging algorithm for general networks. The algorithm is competitive in storage and communication. The competitive ratios are polylogarithmic in the total number of network nodes and the diameter of the network. Johns Hopkins University and Lab. for Computer Science, MIT. Supported by Air Force Contract TNDGAFOSR860078, ARO contract DAAL0386K0171, NSF contract 9114440CCR, DARPA contract N00014J 921799, and a special grant from IBM. EMail: baruch@theory.lcs.mit.edu. y Department of Computer Science, School of Mathematics, TelAviv University, TelAviv 69978, Israel. Supported by a grant from the Israeli Academy of Sciences. Email: yairb@math.tau.ac.il, fiat@math.tau.ac.il 0 1
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 31 (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...
Distributed Paging
 The 1996 Dagstuhl Workshop on Online Algorithms
, 1996
"... . We survey distributed data management problems including distributed paging, file allocation, and file migration. 1 Introduction Many modern information services know no national boundaries. The widespread use of the Internet and Internetrelated applications such as the World Wide Web is growi ..."
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Cited by 16 (0 self)
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. We survey distributed data management problems including distributed paging, file allocation, and file migration. 1 Introduction Many modern information services know no national boundaries. The widespread use of the Internet and Internetrelated applications such as the World Wide Web is growing fantastically on an annual basis. This survey deals with distributed data management problems. Such problems may arise as a memorymanagement problem for a globally addressed shared memory in a multiprocessor system as well as in a distributed network of processors where data files are kept in different sites and may be accessed for information retrieval by dispersed users and applications. In this context, a file may be a conventional single file, a system database, fragments of a database, or any combination of these. When a processor wishes to access a file it must send a request to a processor holding the file and the desired information is transmitted back. The communication cost in...
Competitive Access Time via Dynamic Storage Rearrangement
, 1995
"... We deal with a natural generalization of one of the seminal problems in the study of online computation, list management [ST85a, IRSW91, Irani91]. We consider a doubly linked list with a pointer pointing to the last item accessed. Our goal, as with list management, is to minimize the total number o ..."
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Cited by 4 (0 self)
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We deal with a natural generalization of one of the seminal problems in the study of online computation, list management [ST85a, IRSW91, Irani91]. We consider a doubly linked list with a pointer pointing to the last item accessed. Our goal, as with list management, is to minimize the total number of pointers traversed over a sequence of searches. This problem models issues of dynamic adaptive disk optimization. In this work we initiate the study of this problem in the competitive setting. Our main result is showing nontrivial upper bounds on the competitive ratio. For restricted access patterns we give algorithms that have much better competitive ratios. To complement those bounds we show that there is no constantcompetitive algorithm for the problem with arbitrary access patterns, even against an adversary that does not rearrange its items. Department of Computer Science, Tel Aviv University, Tel Aviv. Research supported in part by a grant from the Israel Academy of Sciences. EM...