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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 380 (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...
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 64 (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 32 (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...
New OnLine Algorithms for the Page Replication Problem
, 1994
"... We present improved competitive online algorithms for the page replication problem and concentrate on important network topologies for which algorithms with a constant competitive ratio can be given. We develop an optimal randomized online replication algorithm for trees and uniform networks; its ..."
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Cited by 21 (4 self)
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We present improved competitive online algorithms for the page replication problem and concentrate on important network topologies for which algorithms with a constant competitive ratio can be given. We develop an optimal randomized online replication algorithm for trees and uniform networks; its competitive ratio is approximately 1.58. This performance holds against oblivious adversaries. We also give a randomized memoryless replication algorithm for trees and uniform networks that is 2competitive against adaptive online adversaries. Furthermore we consider online replication algorithms for rings and present general techniques that transform ccompetitive algorithms for trees into 2ccompetitive algorithms for rings. As a result we obtain a randomized online algorithm for rings that is 3.16competitive. We also derive two 4competitive online algorithms for rings which are either deterministic or randomized and memoryless. Again, the randomized results hold against oblivious ad...
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 17 (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...
Reconfigurable resource scheduling
 In Proceedings of the 18th Symposium on Parallelism in Algorithms and Architectures
, 2006
"... We consider a class of scheduling problems that we refer to as reconfigurable resource scheduling. This class of problems is motivated by emerging applications that involve dynamically allocating a large number of shared resources to a variety of services. We design efficient online algorithms for c ..."
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Cited by 7 (3 self)
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We consider a class of scheduling problems that we refer to as reconfigurable resource scheduling. This class of problems is motivated by emerging applications that involve dynamically allocating a large number of shared resources to a variety of services. We design efficient online algorithms for certain problems in this class. Our goal is to obtain constant competitive online algorithms where the online algorithm is given a constant factor advantage in terms of the number of resources. The main problem considered in this paper is as follows. The input is a sequence of requests, each of which is a set of unit jobs. Each job has a category, and needs to be processed within a fixed delay bound from its arrival, or else it is dropped and we incur a categoryspecific drop cost. A job of a given category can only be executed on a resource configured for that category. A resource can be reconfigured at any time at a fixed reconfiguration cost. Our main result is a constant competitive online algorithm for this problem, which is obtained by the following layered approach. First, we reduce our main problem to the special case in which all jobs arrive at integral multiples of the delay bound. Second, we reduce the latter problem to the special case of unit delay. Third, we reduce the unitdelay problem to a caching problem that we refer to as file caching with remote reads. Our solution to this caching problem generalizes certain existing work in the area of file caching.
Page migration in dynamic networks
, 2005
"... In the last couple of decades, network connected systems have gradually replaced centralized parallel computing machines. To provide smooth operation of network applications, the underlying system has to provide socalled basic services. One of the most crucial services is to provide a transparent a ..."
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Cited by 3 (1 self)
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In the last couple of decades, network connected systems have gradually replaced centralized parallel computing machines. To provide smooth operation of network applications, the underlying system has to provide socalled basic services. One of the most crucial services is to provide a transparent access to data like
On the work function algorithm for two state task systems
, 2007
"... We revisit the known work function online algorithm WFA for metrical task systems in the special case when there are only two states. It is well known that this algorithm is 3 competitive. We offer a slightly modified version of this algorithm, and show that our version exactly mimics the migration ..."
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Cited by 1 (1 self)
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We revisit the known work function online algorithm WFA for metrical task systems in the special case when there are only two states. It is well known that this algorithm is 3 competitive. We offer a slightly modified version of this algorithm, and show that our version exactly mimics the migration pattern of the best possible offline algorithm, though the timing of the migration events is somewhat different in these two algorithms. We use this to give a refined bound on the cost of WFA in terms of the cost of the optimal offline algorithm. Specifically, we partition the cost of the optimal algorithm to a fixed cost F, inefficiency cost I and migration cost M. The cost of our algorithm is at most F + I + 3M. This implies that our version of WFA does not only have a worst case competitive ratio at most 3 (which is best possible) but additionally enjoys better competitive ratios on “typical” input sequences. The current study was motivated by practical problem. We present preliminary experimental evidence that indicates that the algorithm works well in practice. 1