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77
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.
An Adaptive Data Replication Algorithm
 ACM Transactions on Database Systems
, 1997
"... This paper addresses the performance of distributed database systems. Specifically, we present an algorithm for dynamic replication of an object in distributed systems. The algorithm is adaptive in the sense that it changes the replication scheme of the object (i.e. the set of processors at which th ..."
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Cited by 154 (0 self)
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This paper addresses the performance of distributed database systems. Specifically, we present an algorithm for dynamic replication of an object in distributed systems. The algorithm is adaptive in the sense that it changes the replication scheme of the object (i.e. the set of processors at which the object is replicated), as changes occur in the readwrite pattern of the object (i.e. the number of reads and writes issued by each processor). The algorithm continuously moves the replication scheme towards an optimal one. We show that the algorithm can be combined with the concurrency control and recovery mechanisms of a distributed database management system. The performance of the algorithm is analyzed theoretically and experimentally. On the way we provide a lower bound on the performance of any dynamic replication algorithm.
Competitive NonPreemptive Call Control
"... We deal with randomized competitive algorithms for nonpreemptive call control on treelike switching networks. We give an optimal O(log n) competitive algorithm for nonpreemptive call scheduling on trees. We then extend the problem to include variable call rates, call durations, and arbitrary call ..."
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Cited by 110 (8 self)
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We deal with randomized competitive algorithms for nonpreemptive call control on treelike switching networks. We give an optimal O(log n) competitive algorithm for nonpreemptive call scheduling on trees. We then extend the problem to include variable call rates, call durations, and arbitrary call benefits, and obtain a polylog competitive algorithm. We also show that many similar algorithms for different problems that can deal with constant values of parameters such as rates and benefits can be transformed into randomized algorithms that can deal with varying values of the parameters.
Data Replication for Mobile Computers
, 1994
"... Users of mobile computers will soon have online access to a large number of databases via wireless networks. Because of limited bandwidth, wireless communication is more expensive than wire communication. In this paper we present and analyze various static and dynamic data allocation methods. The ob ..."
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Cited by 77 (5 self)
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Users of mobile computers will soon have online access to a large number of databases via wireless networks. Because of limited bandwidth, wireless communication is more expensive than wire communication. In this paper we present and analyze various static and dynamic data allocation methods. The objective is to optimize the communication cost between a mobile computer and the stationary computer that stores the online database. Analysis is performed in two cost models. One is connection (or time) based, as in cellular telephones, where the user is charged per minute of connection. The other is message based, as in packet radio networks, where the user is charged per message. Our analysis addresses both, the average case and the worst case for determining the best allocation method. 0 1 Introduction Users of mobile computers, such as palmtops, notebook computers and personal communication systems, will soon have online access to a large number of databases via wireless networks. The ...
Data Partitioning and Load Balancing in Parallel Disk Systems
, 1994
"... Parallel disk systems provide opportunities for exploiting I/O parallelism in two possible ways, namely via interrequest and intrarequest parallelism. In this paper we discuss the main issues in performance tuning of such systems, namely striping and load balancing, and show their relationship to ..."
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Cited by 62 (8 self)
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Parallel disk systems provide opportunities for exploiting I/O parallelism in two possible ways, namely via interrequest and intrarequest parallelism. In this paper we discuss the main issues in performance tuning of such systems, namely striping and load balancing, and show their relationship to response time and throughput. We outline the main components of an intelligent file system that optimizes striping by taking into account the requirements of the applications, and performs load balancing by judicious file allocation and dynamic redistributions of the data when access patterns change. Our system uses simple but effective heuristics that incur only little overhead. We present performance experiments based on synthetic workloads and reallife traces.
Approximation Algorithms for Data Placement in Arbitrary Networks
 in Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms
, 2001
"... Abstract We develop approximation algorithms for the problem of placing replicated data in arbitrary networks, where the nodes may both issue requests for data objects and have capacity for storing data objects, so as to minimize the average dataaccess cost. We introduce the data placement problem ..."
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Cited by 59 (2 self)
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Abstract We develop approximation algorithms for the problem of placing replicated data in arbitrary networks, where the nodes may both issue requests for data objects and have capacity for storing data objects, so as to minimize the average dataaccess cost. We introduce the data placement problem tomodel this problem. We have a set of caches F, a set of clients D, and a set of data objects O. Each cache i can store at most ui data objects. Each client j 2 D has demand dj for a specific data object o(j) 2 O and has to be assigned to a cache that stores that object. Storing an object o in cache i incurs astorage cost of f oi, and assigning client j to cache i incurs an access cost of djcij. The goal is to find aplacement of the data objects to caches respecting the capacity constraints, and an assignment of clients
EnergyEfficient Algorithms for . . .
, 2007
"... We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good respons ..."
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Cited by 59 (2 self)
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We study scheduling problems in batteryoperated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadlinebased settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variablespeed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unitsize jobs. We devise a deterministic constant competitive online algorithm and show that
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.