Algorithms and Computation: 11th International Conference, by Jean-Daniel Boissonnat (auth.), Gerhard Goos, Juris

By Jean-Daniel Boissonnat (auth.), Gerhard Goos, Juris Hartmanis, Jan van Leeuwen, D. T. Lee, Shang-Hua Teng (eds.)

The papers during this quantity have been chosen for presentation on the 11th Annual foreign Symposium on Algorithms and Computation (ISAAC 2000), hung on 18{20 December, 2000 on the Institute of knowledge technological know-how, Academia Sinica, Taipei, Taiwan. prior conferences have been held in Tokyo (1990), Taipei (1991), Nagoya (1992), Hong Kong (1993), Beijing (1994), Cairns (1995), Osaka (1996), Singapore (1997), Taejon (1998), and Chennai (1999). Submissions to the convention this yr have been performed completely electro- cally. because of the superb software program built by way of the Institute of data technological know-how, Academia Sinica, we have been capable of perform nearly all verbal exchange through the area vast internet. based on the decision for papers, a complete of 87 prolonged abstracts have been submitted from 25 international locations. every one submitted paper used to be dealt with by means of not less than 3 application committee individuals, with the help of a couple of exterior reviewers, as indicated by way of the referee record present in the complaints. there have been many extra applicable papers than there has been house on hand within the symposium application, which made this system committee’s activity super di cult. eventually forty six papers have been chosen for presentation on the Symposium. as well as those contributed papers, the convention additionally integrated invited shows via Dr. Jean-Daniel Boissonnat, INRIA Sophia-Antipolis, France and Professor Jin-Yi Cai, collage of Wisconsin at Madison, Wisconsin, united states. it truly is anticipated that the majority of the permitted papers will seem in a extra whole shape in scienti c journals.

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Extra info for Algorithms and Computation: 11th International Conference, ISAAC 2000 Taipei, Taiwan, December 18–20, 2000 Proceedings

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Rn . / Ti , the replacement algorithm OPTh chooses the locaFor a cache miss ri ∈ tion in the cache whose forward distance is largest. That is, it chooses s = OPTh (Ti , Qi , ri ) if fi (Ti [s]) = max1≤j≤h fi (Ti [j]), where ties are broken arbitrarily. Belady [2] showed that for any request sequence R, the OPT algorithm minimizes the total number of misses. 4 The Adversary’s Strategy Before presenting our analytical results in Sect. 5, we first develop a framework for describing and analyzing the oblivious adversary.

Theorem 2. For each strategy (S, Z), a request sequence R = r1 , . . , rn exists such that 1. request ri is a hit if and only if outcome zi = 1, and 2. running OPT|slots(S)| on request sequence R produces the slot sequence S. Proof. Let S = s1 , . . , sn , Z = z1 , . . , zn , and h = |slots(S)|. We shall show that a request sequence R = r1 , . . , rn satisfying both conditions exists. We construct request sequence R by the inductive definition: ri = i rprev(S,i) if zi = 0, if zi = 1. (1) The request sequence R is well defined, because the definition of prev(S, i) depends on r1 , r2 , .

28 P. Bose et al. Bottom-up Strategy: 1. , if u precedes v then pu ≤ pv . 2. Assign the highest probability leaf to the root. 3. Assign the remaining leaves recursively as follows. Consider an unassigned leaf, say l, of highest probability. Find its furthest unassigned ancestor, say u. Assign l to u. A simple analysis of the performance of the algorithm is as follows. Let u1 , u2 , . . , (n−1)st highest probability in the given probability distribution p. It is easy to see that the resulting gain ≥ (n − 1)pu1 + (n − 2)pu2 + · · · + (n − (n − 1))pun−1 n−1 n−1 = n i=1 pui − i=1 ipui .

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