Results 1  10
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25
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...
Competitive Distributed File Allocation
, 1993
"... This paper deals with the file allocation problem [BFR92] concerning the dynamic optimization of communication costs to access data in a distributed environment. We develop a dynamic file reallocation strategy that adapts online to a sequence of read and write requests whose location and relative ..."
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Cited by 105 (12 self)
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This paper deals with the file allocation problem [BFR92] concerning the dynamic optimization of communication costs to access data in a distributed environment. We develop a dynamic file reallocation strategy that adapts online to a sequence of read and write requests whose location and relative frequencies are completely unpredictable. This is achieved by replicating the file in response to read requests and migrating the file in response to write requests while paying the associated communications costs, so as to be closer to processors that access it frequently. We develop first explicit deterministic online strategy assuming existence of global information about the state of the network; previous (deterministic) solutions were complicated and more expensive. Our solution has (optimal) logarithmic competitive ratio. The paper also contains the first explicit deterministic data migration [BS89] algorithm achieving the best known competitive ratio for this problem. Using somewhat ...
Competitive Analysis of Randomized Paging Algorithms
, 2000
"... The paging problem is defined as follows: we are given a twolevel memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded but slow memory. At each given time step, a request to an item is issued. Given a request to an item p ..."
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Cited by 62 (9 self)
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The paging problem is defined as follows: we are given a twolevel memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded but slow memory. At each given time step, a request to an item is issued. Given a request to an item p,amiss occurs if p is not present in the fast memory. In response to a miss, we need to choose an item q in the cache and replace it by p. The choice of q needs to be made online, without the knowledge of future requests. The objective is to design a replacement strategy with a small number of misses. In this paper we use competitive analysis to study the performance of randomized online paging algorithms. Our goal is to show how the concept of work functions, used previously mostly for the analysis of deterministic algorithms, can also be applied, in a systematic fashion, to the randomized case. We present two results: we first show that the competitive ratio of the marking algorithm is ex...
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 58 (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
Placement Algorithms for Hierarchical Cooperative Caching
, 1999
"... Consider a hierarchical network in which each node periodically issues a request for an object drawn from a fixed set of unitsize objects. Suppose further that the following conditions are satisfied: the frequency with which each node accesses each object is known; each node has a cache of known ca ..."
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Cited by 54 (7 self)
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Consider a hierarchical network in which each node periodically issues a request for an object drawn from a fixed set of unitsize objects. Suppose further that the following conditions are satisfied: the frequency with which each node accesses each object is known; each node has a cache of known capacity; any cache can be accessed by any node; any request is satisfied by the closest node with a copy of the desired object, at a cost proportional to the distance between the accessing node and the closest copy. In such an environment, it is desirable to fill the available cache space with copies of objects in such a way that the average access cost is minimized. We provide both exact and approximate polynomialtime algorithms for this hierarchical placement problem. Our exact algorithm is based on a reduction to mincost flow, and does not appear to be practical for large problem sizes. Thus we are motivated to search for a faster approximation algorithm. Our main result is a simple constantfactor approximation algorithm for the hierarchical placement problem that admits an efficient distributed implementation.
Online Generalized Steiner Problem
, 1996
"... The Generalized Steiner Problem (GSP) is defined as follows. We are given a graph with nonnegative weights and a set of pairs of vertices. The algorithm has to construct minimum weight subgraph such that the two nodes of each pair are connected by a path. Offline generalized Steiner problem ap ..."
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Cited by 40 (5 self)
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The Generalized Steiner Problem (GSP) is defined as follows. We are given a graph with nonnegative weights and a set of pairs of vertices. The algorithm has to construct minimum weight subgraph such that the two nodes of each pair are connected by a path. Offline generalized Steiner problem approximation algorithms were given in [AKR91, GW92]. We consider the online generalized Steiner problem, in which pairs of vertices arrive online and are needed to be connected immediately. We give a simple O(log² n) competitive deterministic online algorithm. The previous best algorithm was O( p n log n) competitive [WY93]. We also consider the network connectivity leasing problem which is a generalization of the GSP. Here edges of the graph can be either bought or leased for different costs. We provide simple randomized O(log² n) competitive algorithm based on the online generalized Steiner problem result.
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...
Exploiting Locality for Data Management in Systems of Limited Bandwidth
 IN PROCEEDINGS OF THE 38TH ANNUAL IEEE SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE
, 1997
"... This paper deals with data management in computer systems in which the computing nodes are connected by a relatively sparse network. We consider the problem of placing and accessing a set of shared objects that are read and written from the nodes in the network. These objects are, e.g., global varia ..."
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Cited by 25 (3 self)
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This paper deals with data management in computer systems in which the computing nodes are connected by a relatively sparse network. We consider the problem of placing and accessing a set of shared objects that are read and written from the nodes in the network. These objects are, e.g., global variables in a parallel program, pages or cache lines in a virtual shared memory system, shared files in a distributed file system, or pages in the World Wide Web. A data management strategy consists of a placement strategy that maps the objects (possibly dynamically and with redundancy) to the nodes, and an access strategy that describes how reads and writes are handled by the system (including the routing). We investigate static and dynamic data management strategies. In the static model, we assume that we are given an application for which the rates of read and write accesses for all nodeobject pairs are known. The goal is to calculate a static placement of the objects to the nodes in the ne...
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 20 (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...
Approximation Algorithms for Data Management in Networks
, 2001
"... This paper deals with static data management in computer systems connected by networks. A basic functionality in these systems is the interactive ..."
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Cited by 15 (0 self)
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This paper deals with static data management in computer systems connected by networks. A basic functionality in these systems is the interactive