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24
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 ...
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
Approximation via costsharing: a simple approximation algorithm for the multicommodity rentorbuy problem
 In IEEE Symposium on Foundations of Computer Science (FOCS
, 2003
"... We study the multicommodity rentorbuy problem, a type of network design problem with economies of scale. In this problem, capacity on an edge can be rented, with cost incurred on a perunit of capacity basis, or bought, which allows unlimited use after payment of a large fixed cost. Given a graph ..."
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Cited by 46 (6 self)
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We study the multicommodity rentorbuy problem, a type of network design problem with economies of scale. In this problem, capacity on an edge can be rented, with cost incurred on a perunit of capacity basis, or bought, which allows unlimited use after payment of a large fixed cost. Given a graph and a set of sourcesink pairs, we seek a minimumcost way of installing sufficient capacity on edges so that a prescribed amount of flow can be sent simultaneously from each source to the corresponding sink. The first constantfactor approximation algorithm for this problem was recently given by Kumar et al. (FOCS ’02); however, this algorithm and its analysis are both quite complicated, and its performance guarantee is extremely large. In this paper, we give a conceptually simple 12approximation algorithm for this problem. Our analysis of this algorithm makes crucial use of cost sharing, the task of allocating the cost of an object to many users of the object in a “fair ” manner. While techniques from approximation algorithms have recently yielded new progress on cost sharing problems, our work is the first to show the converse— that ideas from cost sharing can be fruitfully applied in the design and analysis of approximation algorithms. 1
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 14 (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 OnLine Algorithms for Distributed Data Management
, 1999
"... . Competitive online algorithms for data management in a network of processors are studied in this paper. A data object such as a file or a page of virtual memory is to be read and updated by various processors in the network. The goal is to minimize the communication costs incurred in serving a se ..."
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Cited by 9 (0 self)
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. Competitive online algorithms for data management in a network of processors are studied in this paper. A data object such as a file or a page of virtual memory is to be read and updated by various processors in the network. The goal is to minimize the communication costs incurred in serving a sequence of such requests. Distributed data management on important classes of networkstrees and bus based networks, are studied. Optimal algorithms with constant competitive ratios and matching lower bounds are obtained. Our algorithms use different interesting techniques such as work functions [9] and "factoring." Key words. online algorithms, competitive analysis, memory management, data management. AMS subject classifications. 68Q20, 68Q25. 1. Introduction. The management of data in a distributed network is an important and much studied problem in management science, engineering, computer systems and theory [3, 11]. Dowdy and Foster [11] give a comprehensive survey of research in th...
Improved algorithms for dynamic page migration
 In Proc. of the 22nd Symp. on Theoretical Aspects of Computer Science (STACS
, 2005
"... Abstract The dynamic page migration problem [4] is defined in a distributed network of n mobile nodes sharing one indivisible memory page of size D. During runtime, the nodes can both access a unit of data from the page and move with a constant speed, thus changing the costs of communication. The pr ..."
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Cited by 6 (5 self)
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Abstract The dynamic page migration problem [4] is defined in a distributed network of n mobile nodes sharing one indivisible memory page of size D. During runtime, the nodes can both access a unit of data from the page and move with a constant speed, thus changing the costs of communication. The problem is to compute online a schedule of page movements to minimize the total communication cost. In this paper we construct and analyze the first deterministic algorithm for this problem. We prove that it achieves an (up to a constant factor) optimal competitive ratio O(n · √ D). We show that the randomization of this algorithm improves this ratio to O ( √ D · log n) (against an oblivious adversary). This substantially improves an O(n · √ D) upper bound from [4]. We also give an almost matching lower bound of Ω ( √ D · √ log n) for this problem. 1
Dynamic page migration under brownian motion
 In Proc. of the European Conf. in Parallel Processing (EuroPar
, 2005
"... Abstract. We consider Dynamic Page Migration (DPM) problem, one of the fundamental subproblems of data management in dynamically changing networks. We investigate a hybrid scenario, where access patterns to the shared object are dictated by an adversary, and each processor performs a random walk in ..."
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Cited by 6 (4 self)
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Abstract. We consider Dynamic Page Migration (DPM) problem, one of the fundamental subproblems of data management in dynamically changing networks. We investigate a hybrid scenario, where access patterns to the shared object are dictated by an adversary, and each processor performs a random walk in X. We extend the previous results of [4]: we develop algorithms for the case where X is a ring, and prove that with high probability they achieve a competitive ratio of Õ(min { 4 √ D, n}), where D is the size of the shared object and n is the number of nodes in the network. These results hold also for any ddimensional torus or mesh with diameter at least ˜ Ω ( √ D). 1
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 5 (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.