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By Amitabha Bagchi, Adam L. Buchsbaum, Michael T. Goodrich (auth.), Prosenjit Bose, Pat Morin (eds.)

This publication constitutes the refereed court cases of the thirteenth Annual overseas Symposium on Algorithms and Computation, ISAAC 2002, held in Vancouver, BC, Canada in November 2002.

The fifty four revised complete papers awarded including three invited contributions have been conscientiously reviewed and chosen from as regards to one hundred sixty submissions. The papers disguise all appropriate issues in algorithmics and computation, particularly computational geometry, algorithms and information constructions, approximation algorithms, randomized algorithms, graph drawing and graph algorithms, combinatorial optimization, computational biology, computational finance, cryptography, and parallel and distributedd algorithms.

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M KIOP T (A) = Ω(E( i=1 vCb(A) (b(i)) (wb(A) (b(i)))) This follows from fact 2. 30 J. Iacono m KIOP T (A) = Ω(E( i=1 vCb(A) (b(i)) (w(i)) Since w is unaffected by a bijection. m KIOP T (A) = Ω(E( i=1 vR(w(i)) (w(i)) Since a sequence of distinct numbers passed through a random bijection is just a random sequence of distinct numbers. Now assume E(vR(i) (i)) = Ω(log i) (this will be proven as a lemma below). We can then conclude m KIOP T (A) = Ω(E( i=1 log w(i)) This is Theorem 1. Thus to prove Theorem 1, all that remains is the following Lemma: Lemma 4.

Gupta, and J. S. Vitter. Higher Order Entropy Analysis of Compressed Suffix Arrays. In DIMACS Workshop on Data Compression in Networks and Applications, March 2002. 6. R. Grossi and J. S. Vitter. Compressed Suffix Arrays and Suffix Trees with Applications to Text Indexing and String Matching. In 32nd ACM Symposium on Theory of Computing, pages 397–406, 2000. 7. L. Hui. Color Set Size Problem with Applications to String Matching. In Proc. of the 3rd Annual Symposium on Combinatorial Pattern Matching (CPM’92), LNCS 644, pages 227–240, 1992.

P r 0 • Reca11 fr0m 5ect10n 3 that t0 wa5 ch05en 50 that d(5, x) E [t0,t0 + n0rm(x)). L1ne5 1 and 2 9uarantee that y 15 never 6ucketed 1n a h19her 6ucket than 1D(u) t0, We 0n1y need t0 5h0w that 1n L1ne 1, y 15 n0t 6ucketed 6ef0re L n0rm(x) J" 6ucket 1d(*~u) t0 • - 2 . ~(~), u51n9 the 1ne4ua11ty d( 5, :c) < t0 + n0rm( :c), we a150 have d~fJ(Qy ) > d( 5, y ) - t0 - ~ n0rm( :c) . 50 6ucket1n9 y acc0rd1n9 t0 d~ff(Qy) can put 1t at m05t [~] 2 6ucket5 6ef0re 6ucket ~d(~,~) t01 F0r the fa5t part 0f the Lemma, a55ume that 50me L n 0 r m ( x ) J" Q E Qy 15 a 5uff1x 0f the 5h0rte5t 5-t0-Cy path.

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