A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. In ACM STOC, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....for the synthesis of such walks, and employ it to design competitive on line algorithms. IBM T.J. Watson Research Center, Yorktown Heights, NY 10598. AT T Bell Laboratories, Murray Hill, NJ 07974. 1 Overview Much recent work has dealt with the competitive analysis of on line algorithms [5, 16, 18]. In this paper we study the design of randomized on line algorithms. We show here that the synthesis of random walks on graphs with positive real costs on theirs edges is related to the design of these randomized on line algorithms. We develop methods for the synthesis of such random walks, and ....

....previous moves, and the next cat move depends only on its current position. Some special cases of the cat and mouse game have been studied by Baeza Yates et al. 1] We show that this cat and mouse game is at the core of many other on line algorithms that have evoked tremendous interest of late [3, 4, 5, 8, 9, 11, 18, 20, 21, 22]. We consider two settings. The first is the k server problem, defined in [18] An on line algorithm manages k mobile servers located at the vertices of a graph G whose edges have positive real lengths; it has to satisfy on line a sequence of requests for service at vertex v i , i = 1; 2; ....

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. Journal of the ACM, 39:745--763, 1992.

....finds the mouse. This strategy is very simple, and memoryless: the cat need not remember its previous moves, and the next cat move depends only on its current position. We show that this cat and mouse game is at the core of many other online algorithms that have evoked tremendous interest of late [2, 3, 4, 7, 8, 10, 14, 16, 17, 18]. We consider two settings. The first is the k server problem, defined in [14] An on line algorithm manages k mobile servers located at the nodes of a graph G whose edges have positive real lengths; it has to satisfy a sequence of requests for service at node v i , i = 1; 2; by moving a ....

.... 1 nodes. This includes all previously known cases where the conjecture was proven true, as well as many new cases. We do so with a single unified theory that of resistive inverses. The algorithm is very simple, and memoryless. The other setting is the metrical task system (MTS) defined in [4]. A MTS consists of a weighted graph (the nodes of the graph are states, and edge weights are the costs of moving between states) The algorithm occupies one state at any time. A task is represented by a vector (c 1 ; c n ) where c i is the cost of processing the task in state i. The ....

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. Journal of the ACM, 39:745--763, 1992.

....we may also need to incur some kind of movement cost (we will discuss this more fully in Section 3. 3) This notion of an on line algorithm having state, with a cost for moving between states, is captured by the Metrical Task Slstem (MTS) problem studied in the On line Algorithms literature [5, 12]. In this problem, we imagine the on line algorithm as controlling a system that can be in one of n states or configurations, with some distance metric d among the states specifying the cost of moving from one state to another. This system incrementally receives a sequence of tasks, where each ....

....of segments in P. We will seek to achieve this for a and a2 as small as possible. The easier goal of competing against the best single expert is a restriction of the partitioning bound to the case kp 1. 2.2. The MTS problem and the competitive ratio In the Metrical Task System (MTS) problem [5, 12], an on linc algorithm controls a system with n states located at points in a space with distance metric d. The algorithm receives, one at a time, a sequence of tasks, each of which has a cost vector specifying the cost of performing the task in each state. Say the system currently occupies state ....

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. J of He ACM, 39(4):745 763, 1992.

....B ela Bollob as The University of Memphis Memphis, TN 38152 bollobas msci.memphis.edu Manor Mendel Tel Aviv University Tel Aviv, Israel mendelma tau.ac. il Abstract This paper gives a nearly logarithmic lower bound on the randomized competitive ratio for the Metrical Task Systems model [BLS92] This implies a similar lower bound for the extensively studied K server problem. Our proof is based on proving a Ramsey type theorem for metric spaces. In particular we prove that in every metric space there exists a large subspace which is approximately a hierarchically well separated ....

....1 Introduction This paper deals with the analysis of the performance of randomized online algorithms in the context of two fundamental online problems, the problem of metrical task systems and the K server problem. A metrical task system (MTS) introduced by Borodin, Linial, and Saks [BLS92] is a system that may be in one of a set of n internal states. The aim of the system is to perform a certain sequence of tasks. The performance of each task has a certain cost that depends on the task and the state of the system. The system, also called the server, may switch states; the cost of ....

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A. Borodin, N. Linial, and M. Saks, An optimal online algorithm for metrical task systems, J. Assoc. Comput. Mach. 39 (1992), no. 4, 745-763.

....incur loss by selecting a bad expert, but it also incurs loss for moving between experts. This notion of an on line algorithm having state, with a cost for moving between states, is captured by a problem studied in the On line Algorithms literature called the Metrical Task System (MTS) problem [BLS92, IS95] In this problem, we imagine the on line algorithm is controlling a system that can be in one of n states or configurations. This system is given a sequence of tasks, where each task has a cost vector specifying the cost of performing the task in each state of the system. There is also a ....

....the other has an unbounded competitive ratio. Finally, in Section 5 we present an empirical comparison of these algorithms and others for the process migration problem. 2 Definitions and general relations 2. 1 The MTS problem and the competitive ratio In the Metrical Task System (MTS) problem [BLS92, IS95] an on line algorithm controls a system with n states located at points in a space with distance metric d. The algorithm receives, one at a time, a sequence of tasks, each a cost vector specifying the cost of performing the task in each state. Say the system currently occupies state i and, ....

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. J of the ACM, 39(4):745--763, 1992.

....case of paging, each request to a page of memory requires that page to be present in the cache; in the k server problem one server must be present in one speci ed location to serve the request. The problems that we consider are a special case of the more general notion of Metrical Task Systems [6] that allows to model a great variety of on line problems. However, the generality of that approach implies that the results that have been proved are rather negative results. In fact, competitive algorithms with small constant competitiveness coecients have been found for di erent versions of the ....

.... coecients have been found for di erent versions of the paging and the k server problem [7, 8, 10, 11, 12, 13, 15, 17, 18, 20] On the other side, a lower bound on the competitiveness of any on line algorithm for Metrical Task Systems has been proved that is linear in the number of di erent states [6]. For the problems considered in this paper, the number of states is exponential in the size of the cache. However, the competitiveness coecients that we obtain are polynomial in the size of the cache. Besides their theoretical interest, the problems that we consider are motivated by the memory ....

A. Borodin, N. Linial, and M. Saks, An optimal online algorithm for metrical task systems, Proc. 19th Annual ACM Symposium on Theory of Computing 373-382 (1987).

....of the competitive ratio decision criterion. Competitive analysis has been applied to a variety of classical problems in computer science, such as the kserver problem [ Koutsoupias and Papadimitriou, 1995 ] and paging [ Fiat et al. 1991 ] as well as to more general algorithmic problems [ Borodin et al. 1992 ] In all of these studies the environment that the agent acts in is non strategic, and therefore does not assume to follow any rational behavior. In this paper we extend the concept of competitive analysis to the context of multiagent systems. In a multi agent system the environment In fact, ....

A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. Journal of the ACM, 39:745--763, 1992.

....some requests and rejecting others with the goal of maximizing the total resource utilization. The requests or packets must be serviced online in these applications since the future arrival sequence is generally not known. We use competitive analysis to measure the quality of our algorithms [13, 11, 6]; we consider both deterministic as well as randomized algorithms. We consider the oblivious competitive ratio in which the input sequence is selected independently of the random choices of the algorithm [5] Table 1: Summary of Results. We require that k is a real number greater than 1 and ....

....Pr[J 2 oe] Delta jJ j, where the probability that oe occurs is with respect to the algorithm A, meaning the probability that A produces schedule oe given S. We let GA (S) J2S GA (J ) When the algorithm being studied is clear, we just use G(J) and G(S) We use standard competitive analysis [13, 11, 6] to evaluate our algorithms. J j J j Figure 1: In the left drawing J j blocks J i , and in the right one J j covers J i . If J j = J then by our definition of blocking, J j blocks J i . Namely, let oe be an optimal solution (constructed by a computationally unbounded off line ....

A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. Communications of the ACM, 39(4):745--763, 1992. 19

....we carry out our analysis assuming that position m coincides with position 0, that is, the encyclopedia is circular. This assumption eliminates move (3) and clarifies our arguments. We then show how to transfer our results back to the linear case. We analyze the competitiveness of our algorithms [3, 9, 11, 13]. That is, we compare the performance of an online algorithm against the performance of an optimal offline algorithm that sees all requests in advance. An algorithm is called c competitive if its cost on any sequence of n requests is at most O(1) greater than c times the offline algorithm s cost. ....

....no assumptions about the distribution or correlation of requests are made; however, it measures performance relative to what is achievable by an omniscient algorithm, rather than in absolute terms. A discretized version of our problem is an example of a task system as defined by Borodin et al. [3]. Borodin et al., however, study a more general model in which the costs of serving requests rather than just request locations may be chosen by an adversary, so their bounds have no nontrivial implications for our problem. Other related work includes a number of recent papers on server ....

A. Borodin, N. Linial, and M. Saks, An Optimal Online Algorithm for Metrical Task Systems, 19th ACM Symp. on Theory of Computing , 1987.

....out our analysis assuming that position m coincides with position 0, that is, the encyclopedia is circular. This assumption eliminates move (3) and clarifies our arguments. We then show how to transfer most of our results back to the linear case. We analyze the competitiveness of our algorithms [3, 11, 13, 16]. That is, we compare the performance of an online algorithm against the performance of an optimal offline algorithm that sees all requests in advance. An algorithm is called c competitive if its cost on any sequence of n requests is at most O(1) greater than c times the offline algorithm s cost. ....

....the distribution or correlation of requests are made; however, it measures performance relative to what is achievable by an omniscient algorithm, rather than in absolute terms. 2 1.1. Related Work A discretized version of our problem is an example of a task system as defined by Borodin et al. [3]. Borodin et al. however, study a more general model in which the costs of servicing requests rather than just request locations may be chosen by an adversary, so their bounds have no nontrivial implications for our problem. Other related work includes a number of recent papers on server ....

A. Borodin, N. Linial, and M. Saks, An Optimal Online Algorithm for Metrical Task Systems, 19th ACM Symp. on Theory of Computing , 1987, 373--382.

.... the use of comparative analysis by attacking the question of the power of lookahead in on line problems of the server type: If L is the class of all algorithms with lookahead , and L 0 is the class of on line algorithms, then we show that, in the very general context of metrical task systems [3] we have R(L 0 ; L ) 2 1; that is, the ratio is at most 2 1 for all metrical task systems, and it is exactly 4 E. KOUTSOUPIAS AND C. PAPADIMITRIOU 2 1 for some) while in the more restricted context of paging R(L 0 ; L ) minf 1; kg: 2. Di use Adversaries. The competitive ....

....algorithm for a metrical task system has lookahead if it can base its decision not only on the past, but also on the next requests. All on line algorithms with lookahead comprise the information regime L . Thus, L 0 is the class of all traditional on line algorithms. Metrical task systems [3] are de ned on some metric space M; a server resides on some point of the metric space and can move from point to point. Its goal is to process on line a sequence of tasks T 1 ; T 2 ; The server is free to move to any position before processimg a task, although it has to pay the distance. ....

A. Borodin, N. Linial, and M. E. Saks, An optimal online algorithm for metrical task systems., Proceedings 19th Annual ACM Symposium on Theory of Computing, (1987), pp. 373-82.

....the adversary is ignorant of the outcomes of the random choices made by the online algorithm this adversary is called oblivious. 10 Indeed, it is often the case that randomization (against an oblivious adversary) dramatically improves the competitive performance (see the classical results of [8] and [15] regarding metrical task systems and virtual memory management) As we shall later see randomization empowers the online player also in the search problem. 1.5. Competitive Analysis: A Discussion. The main attraction in using the competitive ratio for analyzing online algorithms is that ....

A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. Journal of the ACM, 39:745--763, 1992. For the conference version see [7]. Optimal Search and One-Way Trading Online Algorithms 139

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. In Proc. 19th Annual ACM Symposium on Theory of Computing, pp. 373-382, 1987.

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. In ACM STOC, 1987.

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task system. Journal of the ACM, 39:745--763, 1992.

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task system. Journal of the ACM, 39:745-763, 1992.

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task system. Journal of the ACM, 39:745-763, 1992.

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. Journal of the ACM, 39:745--763, 1992.

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Allan Borodin, Nathan Linial, and Michael Saks, An optimal online algorithm for metrical task system, Journal of the ACM 39 (1992), 745--763.

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A. Borodin, N. Linial, and M. Saks. An Optimal OnLine Algorithm for Metrical Task Systems. In Proc. of the 19th Ann. ACM Symp on Theory of Computing, pages 373{ 382, May 1987.

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. J. Assoc. Comput. Mach., 39(4):745-763, 1992.

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. Journal of the ACM, 39:745-763, 1992. 25

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A. Borodin, N. Linial, and M. Saks. "An Optimal Online Algorithm for Metrical Task Systems" Proceedings of the 19th Annual ACM Symposium on Theory of Computing, 1987, pp. 373--382.

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. In Proc. 19th Annual ACM Symposium on Theory of Computing, pages 373--382, 1987.

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A. Borodin, N. Linial, and M. Saks. An optimal online algorithm for metrical task systems. In Proceedings of the 19th Annual ACM Symposium on Theory of Computing, pages 373--382, 1987. For the journal version see [8].

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