Steven S. Seiden. A guessing game and randomized online algorithms. In Proceedings of the thirty-second annual ACM symposium on Theory of 41 computing, pages 592-601. ACM Press, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....are the rst ones for OlTrp and L OlDarp. Our algorithms are adaptions of the greedy interval algorithm for onlinescheduling presented in [10, 11] and of the randomized version given in [7] Our lower bound results are obtained by applying Yao s principle in conjunction with a technique of Seiden [13]. An overview of the results is given in Tables 1 and 2. Deterministic UB Previous best UB Deterministic LB OlTrp 6 (Corollary 3.5) 9 [8] real line) 1 2 [8] L OlDarp 6 (Theorem 3.4) 15 [8] real line, server capacity 1) 3 [8] Table 1. Deterministic upper and lower bounds. In Section 2 we ....

....= 4:3281 for OlTrp against an oblivious adversary. ut 5 Lower Bounds In this section we show lower bounds for the competitive ratio of any randomized algorithm against an oblivious adversary for the problem L OlDarp. The basic method for deriving such a lower bound is Yao s principle (see also [6, 12, 13]) Let X be a probability distribution over input sequences = f x : x 2 X g. We denote the expected cost of the deterministic algorithm alg according to the distribution X on by E X [alg( x ) Yao s principle can now be stated as follows. Theorem 5.1 (Yao s principle) Let f alg y : y 2 Y ....

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S. Seiden, A guessing game and randomized online algorithms, Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing, 2000, pp. 592-601.

.... Yao s Principle is to specify a probability distribution X over input sequences such that on average, every deterministic algorithm performs badly, that is, such that E X [ALG y (# x ) is high compared to the expected optimal cost E X [OPT(# x ) In this chapter we use a method proposed in [Sei00] to compute a suitable distribution once our ground set of request sequences has been fixed. 5.2.1 A General Lower Bound for w j C j OLDARP We provide a general lower bound where the metric space is a star, which consists of three rays of length 2 each. The center of the star is the origin, ....

....Hence in what follows it suffices to consider the case y 1. To maximize the expected cost of any deterministic online algorithm on our randomized input sequence, we wish to choose # and a density function p such that min y#[0,1] F(y) is maximized. We use the following heuristic approach (cf. Sei00] Assume that # and the density function p maximizing the minimum have the property that F(y) is constant on [0, 1] Hence F # (y) 0 and F ## (y) 0 for all y (0, 1) Differentiating we find that F # (y) 2 # (1 k) p(x) dx (k 2y)p(y) and F ## (y) 2(k 1)p(y) 2(k ....

S. Seiden, A guessing game and randomized online algorithms, Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing, 2000, pp. 592--601.

....times must be chosen online without knowledge of when future arrivals will occur. Dooly et al. showed that the natural algorithm which waits until the latency since the previous acknowledgement equals the cost of the acknowledgement has a competitive ratio of 2. Subsequently, Seiden [13], and independently Noga [11] obtained a lower bound of e= e Gamma1) on the competitive ratio of randomized online algorithms for this problem. A matching upper bound remained elusive, and in fact no randomized algorithm was known to beat the 2 competitive ratio achieved by the deterministic ....

....achieves a competitive ratio of 2 Gamma 1=m [6] The best bounds currently known on the competitive ratio for deterministic algorithms are an upper bound of approximately 1.92 [1, 8] and a lower bound of approximately 1. 85 [1] For randomized algorithms, there is a lower bound of e e Gamma1 [4, 13]. However, it is currently not known whether there are randomized algorithms that beat the deterministic ones for m large. This is one of the most notorious open problems in online scheduling and we do not resolve it here. However, we are intrigued by the possibility that there may be a ski rental ....

Steven S. Seiden. "A Guessing Game and Randomized Online Algorithms". Proceedings of the thirty-second annual ACM symposium on theory of computing (STOC), 2000, Portland, OR, USA, pp. 592-601.

....course in practice the acknowledgment times must be chosen online without knowledge of when future arrivals will occur. Dooly et al. showed that the natural algorithm which waits until the latency since the previous acknowledgement equals the cost of the acknowledgement is 2 . Subsequently, Seiden [13] and independently Noga [11] got a lower bound of e= e Gamma 1) on the competitive ratio of randomized online algorithms for this problem. A matching upper bound remained elusive, and in fact no randomized algorithm was known to beat the 2competitive ratio achieved by the deterministic ....

....achieves a competitive ratio of 2 Gamma 1=m [6] The best bounds currently known on the competitive ratio for deterministic algorithms are an upper bound of approximately 1.92 [1, 8] and a lower bound of approximately 1. 85 [1] For randomized algorithms, there is a lower bound of e e Gamma1 [4, 13]. However, it is currently not known whether there are randomized algorithms that beat the deterministic ones for m large. This is one of the most notorious open problems in online scheduling and we do not resolve it here. However, we are intrigued by the possibility that there may be a ski rental ....

Steven S. Seiden. "A Guessing Game and Randomized Online Algorithms". Proceedings of the thirty-second annual ACM symposium on theory of computing (STOC), 2000, Portland, OR, USA, pp. 592-601.

.... delivery times [44] scheduling on machines which run at di#erent speeds [19] and scheduling when the online restriction is loosened [54] Investigations currently underway include: algorithms for online page replication [26] and general techniques for proving lower bounds for online algorithms [53]. 5.2.5 Planned Work In addition to continuing his ongoing research, the PI has plans to investigate the following problems in the near future: Paging and caching are some of the most fundamental and practical online problems in computer science. The advent of the world wide web has brought ....

....a strong researcher in theoretical computer science would almost certainly help the LSU Department of Computer Science gain international recognition. The PI has distinguished himself from other researchers in the area of approximation algorithms by: Focusing on the use of randomization [6, 19, 26, 32, 44, 46, 47, 49, 53, 50, 51, 52, 54], which currently is poorly understood. Using computer aided analysis techniques to attack problems which are considered to be very hard [19, 44, 46, 47, 48, 51, 54] While the research approach of the PI is not totally unique, the group of researchers worldwide utilizing such approaches is ....

Seiden, S. S. A guessing game and randomized online algorithms. In Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (May 2000). To appear.

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Steven S. Seiden. A guessing game and randomized online algorithms. In Proceedings of the thirty-second annual ACM symposium on Theory of 41 computing, pages 592-601. ACM Press, 2000.

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S.S. Seiden. A guessing game and randomized online algorithms. Proc. 32nd ACM Symposium on Theory of Computing , 592-601, 2000.

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S. Seiden, A guessing game and randomized online algorithms, Proceedings of the 32nd Annual ACM Symposium on the Theory of Computing, 2000, pp. 592{ 601. 18

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Steven S. Seiden. \A Guessing Game and Randomized Online Algorithms." Proceedings of the thirty-second annual ACM symposium on theory of computing (STOC), 2000, Portland, OR, USA, pp. 592-601.

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