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 data 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 12 months have been performed solely electro- cally. because of the superb software program constructed through the Institute of data technology, Academia Sinica, we have been in a position to perform nearly all conversation through the realm huge internet. in accordance with the decision for papers, a complete of 87 prolonged abstracts have been submitted from 25 nations. every one submitted paper used to be dealt with by means of at the least 3 application committee contributors, with the help of a few exterior reviewers, as indicated through the referee checklist present in the complaints. there have been many extra appropriate papers than there has been house to be had within the symposium software, which made this system committee’s activity 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, collage of Wisconsin at Madison, Wisconsin, united states. it really is anticipated that almost all of the authorised 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**

**Example text**

We next show that Condition 2 holds. We show that si is selected by OPTh at any time i = 1, 2, . . , n. – If zi = 1, then by Condition 1, ri is a hit. In this case, ri = rprev(S,i) , and thus OPTh must select sprev(S,i) . But, by the definition of prev, sprev(S,i) = si , and therefore si is selected. – If zi = 0, then we shall show that OPTh chooses slot si to replace. Recall that s = OPTh (Ti , Qi , ri ) if fi (Ti [s]) = max1≤j≤k fi (Ti [j]), where the Ti are cache states and the Qi are control states (both defined in Sect.

Alon and V. D. Milman, Eigenvalues, expanders and superconcentrators. Proc of the 25th ACM STOC, 320–322. 1984. 7. 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.

Lemma 19. For square integrable function φ on U with U |A∗ (φ) − φ|2 + U U √ |A˜∗ (φ) − φ|2 ≥ (4 − 2 3) φ = 0, U |φ|2 . Proof. By Parseval equality, for square integrable ψ, |ψ|2 = U |aq (ψ)|2 , q where aq (ψ) are the Fourier coefficients. Note that a0 (φ) = U φ = 0. By linearity and Lemma 16, aq (A∗ (φ) − φ) = aq (A∗ (φ)) − aq (φ) = aAq (φ) − aq (φ). Lemma 19 follows from Lemma 18. Recall the definition of β = βB for B ∈ Σ, βB (ξ) = ξB mod 1. Lemma 20. For measurable set Z ⊆ U , ˜ B=A,A −1 µ[Z − βB (Z)] ≥ (2 − Proof.