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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 overseas 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. past 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 carried out fullyyt electro- cally. because of the superb software program built through the Institute of knowledge technological know-how, Academia Sinica, we have been in a position to perform almost all conversation through the realm broad internet. according to the decision for papers, a complete of 87 prolonged abstracts have been submitted from 25 nations. each one submitted paper was once dealt with via a minimum of 3 application committee individuals, with the help of a couple of exterior reviewers, as indicated by way of the referee checklist present in the court cases. there have been many extra applicable papers than there has been house on hand within the symposium application, which made this system committee’s job tremendous 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 by means of Dr. Jean-Daniel Boissonnat, INRIA Sophia-Antipolis, France and Professor Jin-Yi Cai, college of Wisconsin at Madison, Wisconsin, united states. it really is anticipated that almost all of the accredited papers will seem in a extra entire shape in scienti c journals.

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

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N. Alon and J. Spencer, with an appendix by P. Erd¨ os, The Probabilistic Method. 1992. 8. D. Angulin, A note on a construction of Margulis, Information Processing Letters, 8, pp 17–19, (1979). 9. F. R. K. Chung, On Concentrators, superconcentrators, generalized, and nonblocking networks, Bell Sys. Tech J. 58, pp 1765–1777, (1978). 10. O. Gabber and Z. Galil, Explicit construction of linear size superconcentrators. JCSS 22, pp 407–420 (1981). 11. A. Lubotsky, R. Phillip and P. Sarnak, Explicit expanders and the Ramanujan conjectures.

As a consequence, E[T A , p] is also the expected length of the encoding of the leaves of the tree T A represented as code words in a three letter alphabet. Moreover, the resulting encoding is a prefix code. In particular, Shannon’s theorem applies and we have that N 1 1 · pi log(1/pi ). · H(p) = E[T , p] ≥ log 3 log 3 i=1 A (9) We have proved the following theorem. Theorem 7. For any probability distribution p on the leaves of a full binary tree and any assignment of at most one hotlink per source node the expected number of steps to reach a webpage located at a leaf from the root of the tree is at least H(p)/ log 3, where H(p) is the entropy of p.

1 Results of the Paper For arbitrary DAGs we show that the problem is NP-complete. We then prove upper and lower bounds on the expected number of steps to reach a web page located at a leaf of the full binary tree from the root when the weights on the leaves are drawn from one of the following distributions. – Arbitrary: p1 + p2 + · · · + pN = 1. – Uniform: p1 = p2 = · · · = pN = 1/N , – Geometric: pi = a−i , for i = 1, . . , N −1, and pN = 2−(1−a−N )/(1−a−1 ), where a > 1. N – Zipf: pi = iH1N , where HN = i=1 1/i is the harmonic number.

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