Shai Ben-David, Allan Borodin, Richard M. Karp, Gabor Tardos, and Avi Wigderson. On the power of randomization in on-line algorithms. Algorithmica, 11:2-14, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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; ....

....a cost equal to the distance moved by that server. We compare the cost of such an algorithm, to the cost of an adversary that, in addition to moving its servers, also generates the sequence of requests. The competitiveness of an on line algorithm is defined with respect to these costs (Section 8) [3, 21]. It was conjectured in [18] that for every cost matrix there exists a k competitive algorithm for this problem. Repeated attempts to prove this conjecture have met only with limited success [8, 9, 21] We use our optimal random walk to derive optimal randomized k competitive server algorithms in ....

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S. Ben-David, A. Borodin, R.M. Karp, G. Tardos, and A. Wigderson. On the power of randomization in on-line algorithms. Algorithmica, 11(1):2--14, 1994.

....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 ....

....a cost equal to the distance moved by that server. We compare the cost of such algorithm, to the cost of an adversary that, in addition to moving its servers, also generates the sequence of requests. The competitiveness of an on line algorithm is defined with respect to these costs (Section 5) [2, 17]. It was conjectured in [14] that for every cost matrix there exists a k competitive algorithm for this problem. Repeated attempts to prove this conjecture have succeeded only in a few special cases [7, 8, 17] We use our optimal random walk to derive a k competitive server algorithm in two ....

[Article contains additional citation context not shown here]

S. Ben-David, A. Borodin, R.M. Karp, G. Tardos, and A. Wigderson. On the power of randomization in on-line algorithms. Algorithmica, 11(1):2--14, 1994.

....for all w, 2 is a lower bound on the competitive ratio of any deterministic on line layered graph traversal algorithm. Thus arbitrary layered graphs are much harder to traverse than those consisting of disjoint paths. Randomized on line algorithms are addressed in several papers including [BLS, RS, CDRS, FKLMSY, BBKTW, KRR]. An oblivious adversary is one who constructs the sequence of events in advance and deals with the sequence optimally. For this adversary model [BLS] and [FKLMSY] give examples where randomization can improve the competitive ratio exponentially. This adversary models a world in which the on line ....

....randomization can improve the competitive ratio exponentially. This adversary models a world in which the on line algorithm s actions do not themselves influence future events. One can consider a situation where the on line algorithm s actions have a direct influence on the future. In such cases [BBKTW] have shown that randomization cannot improve the competitive ratio more than polynomially. We deal with randomized layered graph traversal algorithms (assuming an oblivious adversary) and present the following results. ffl Section 5 gives a randomized on line algorithm for the disjoint path ....

S. Ben-David, A. Borodin, R.M. Karp, G. Tardos, and A. Wigderson. On the Power of Randomization in On-Line Algorithms. Algorithmica, 11, 1994.

....even for the case of three servers. This was settled by Fiat, Rabani, and Ravid [FRR] who gave a general algorithm with a competitive ratio of at most O(k log k) Grove improved this bound to 2 O(k) Gr] using a simple randomized algorithm, and derandomization techniques of Ben David et al. [BBKTW]. And very recently, Koutsoupias and Papadimitriou [KP] have shown that the work function algorithm proposed by Chrobak and Larmore [CL4] as by well as other researchers, is at most (2k Gamma 1) competitive. In a separate direction, a number of papers extended the set of metric spaces for ....

S. Ben-David, A. Borodin, R. Karp, G. Tardos, A. Wigderson, "On the power of randomization in on-line algorithms," Proc. 22nd ACM Symposium on Theory of Computing, 1990, pp. 379--386. 82

....we prove a lower bound of Omega Gamma n ) on the competitive ratio of any on line algorithm, for some ffl 0. This is fairly easy to show for deterministic algorithms, our main contribution is showing that this holds even for randomized on line algorithms against an oblivious adversary (cf. BBKTW90] Our lower bounds for the on line independent set and the on line edge disjoint paths problems also hold when in the context of benefit problems the use of preemption is allowed to the randomized algorithm. This means that the on line algorithm is allowed to discard a previously chosen element ....

....cost. If A is randomized the goal is to minimize its expected cost over its coin tosses, E(A(oe) Let ON be an on line algorithm (possibly randomized) and OPT be an optimal algorithm for some problem. We say ON is ae competitive [ST85] for a cost problem (against an oblivious adversary (cf. BBKTW90] if there exists a constant a so that for every sequence oe such that OPT(oe) a, E(ON(oe) ae Delta OPT(oe) The value ae is called the competitive ratio of the algorithm. Benefit Problems. In the case of benefit problems A(oe) denotes the benefit of algorithm A, and the goal of the ....

S. Ben-David, A. Borodin, R.M. Karp, G. Tardos and A. Widgerson. On the Power of Randomization in On-line Algorithms. Proc of the 22nd Annual ACM Symposium on Theory of Computing, 1990.

....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 that c is a known integer. Uniform delay is a delay proportional to job length. However, in the last table entry Uniform refers to a delay proportional to dlg jJje for job J. 1.1 Our Results In earlier work, ....

S. Ben-David, A. Borodin, R. Karp, G. Tardos, and A. Wigderson. On the power of randomization in on-line algorithms. Algorithmica, 11(1):2--14, 1994.

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Shai Ben-David, Allan Borodin, Richard M. Karp, Gabor Tardos, and Avi Wigderson. On the power of randomization in on-line algorithms. Algorithmica, 11:2-14, 1994.

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S.Ben-David, A.Borodin, R.Karp, G.Tardos, A.Wigderson. "On the Power of Randomization in On-Line Algorithms", Proceedings of the 22nd ACM STOC, pp. 379--386, 1990. 15

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S. Ben-David, A. Borodin, R.M. Karp, G. Tardos, and A. Wigderson. On the power of randomization in on-line algorithms. In Proc.of the 22nd Ann. ACM Symp. on Theory of Computing, pages 379--386, May 1990.

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S. Ben-David, A. Borodin, R.M. Karp, G. Tardos, A. Widgerson. On the power of randomization in on-line algorithms. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pages 379-386, 1990.

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S. Ben-David, A. Borodin, R. M. Karp, G. Tardos, and A. Wigderson, On the power of randomization in on-line algorithms, Algorithmica, 11 (1994), pp. 2--14.

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S. Ben-David, A. Borodin, R. Karp, G. Tardos, A. Wigderson, "On the power of randomization in on-line algorithms," Proc. 22nd ACM Symposium on Theory of Computing, 1990, pp. 379--386.

No context found.

S. Ben-David, A. Borodin, R. Karp, G. Tardos, and A. Wigderson. On the power of randomization in on-line algorithms. Algorithmica, 11(1):2--14, 1994.

No context found.

S. Ben-David, A. Borodin, R. M. Karp, G. Tardos, and A. Widgerson. On the power of randomization in on-line algorithms. In Proc. 22nd Symp. Theory of Computing (STOC), pages 379--386. ACM, 1990.

No context found.

S. Ben-David, A. Borodin, R. M. Karp, G. Tardos, and A. Wigderson. On the power of randomization in on-line algorithms. Algorithmica, 11:2-14, 1994.

No context found.

S. Ben-David, A. Borodin, R.M. Karp, G. Tardos and A. Widgerson, On the power of randomization in on-line algorithms. Proc of the 22nd Annual ACM Symposium on Theory of Computing, pp. 379-386, 1990.

No context found.

S. Ben-David, A. Borodin, R.M. Karp, G. Tardos and A. Widgerson, "On the power of randomization in on-line algorithms", Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pp. 379-386, 1990. 25

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S. Ben-David, A. Borodin, R.M. Karp, G. Tardos, and A. Widgerson. On the power of randomization in on-line algorithms. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, 1990.

No context found.

S. Ben-David, A. Borodin, R. M. Karp, G. Tardos, and A. Wigderson, On the power of randomization in on-line algorithms, Algorithmica 11 (1994), 2--14.

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Shai Ben-David, Allan Borodin, Richard Karp, Gabar Tardos, and Avi Wigderson, On the power of randomization in on-line algorithms, Algorithmica 11 (1994), no. 1, 2-14.

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