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

This booklet constitutes the refereed complaints 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 offered including three invited contributions have been conscientiously reviewed and chosen from on the subject of a hundred and sixty submissions. The papers disguise all suitable 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.

**Read or Download Algorithms and Computation: 13th International Symposium, ISAAC 2002 Vancouver, BC, Canada, November 21–23, 2002 Proceedings PDF**

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**Extra resources for Algorithms and Computation: 13th International Symposium, ISAAC 2002 Vancouver, BC, Canada, November 21–23, 2002 Proceedings**

**Sample text**

KIOP T (A) = Θ( i=1 log w(ai )) The proof of this theorem is the subject of Section 2. Corollary 1 Splay trees are key-independently optimal This is immediate, since splay trees have the working set property. If the key values in a given application are assigned randomly, then no binary search tree can be expected to execute A more than a constant multiplicative factor faster than splay trees, even with complete foreknowledge of the access sequence, and inﬁnite preprocessing time. 2 Proof of Main Result Theorem 1 The working set property and key-independent optimality are m asymptotically the same.

8ecau5e we are attempt1n9 t0 6ucket y, d(5, x) mu5t a1ready 6e kn0wn. Let P~f den0te the 5h0rte5t 5-t0-f path (wh1ch 15 a150 the 5h0rte5t 5-t0-C~ path). 5 . . . 1. ,v1},and a ta11 ( v 1 , . . , v j } . Def1n1t10n 1. Let Qy 6e the 5et 0f path5 {(v0,... ,v1,... ,~d ~ 6 ~ (111) ~5 ~ c~ and ( ~ , . . , ~5) ~ m ( y ) 8ucket1n9 y 6y 1t5 D-va1ue 15 e4u1va1ent t0 e5t1mat1n9 D ( y ) - d ( 5 , f), h0wever we 9enera11y w111 n0t have en0u9h 1nf0rrnat10n t0 d0 th15. 0 u r 501ut10n 15 n0t t0 f0cu5 501e1y 0n the current path w1th 1en9th D(y), 6ut t0 e5t1mate the d15tance 0f many hyp0thet1ca11y 5h0rte5t path5 fr0m 5 t0 C~.

Since the deﬁnition of w(x) does not take into account the key values m m at all, i=1 log wi (ai ) = i=1 log w(b(ai )) for every bijection b, including, of course, a randomly chosen one. Thus since splay trees are a binary search tree m structure that will execute b(A) in time O( i=1 log w(ai )), this is an upper bound on KIOP T (A). Lemma 3. KIOP T (A) = Ω( m i=1 log w(ai )) Our lower bound is based upon the second lower bound of Wilbur found in [11]. Given a sequence A and j < i we deﬁne the untouched region at j of i in A, uA (i, j) to be the largest interval (x, y) that contains aj and that no element of (x, y) is in aj .