Algorithms and Computation: 10th International Symposium, by Alok Aggarwal, C. Pandu Rangan

By Alok Aggarwal, C. Pandu Rangan

This ebook constitutes the refereed complaints of the tenth overseas Symposium on Algorithms and Computation, ISAAC'99, held in Chennai, India, in December 1999.
The forty revised complete papers awarded including 4 invited contributions have been rigorously reviewed and chosen from seventy one submissions. one of the themes lined are information buildings, parallel and allotted computing, approximation algorithms, computational intelligence, on-line algorithms, complexity concept, graph algorithms, computational geometry, and algorithms in perform.

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Extra info for Algorithms and Computation: 10th International Symposium, ISAAC’99 Chennai, India, December 16–18, 1999 Proceedings

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The width of a down-up pair is the time distance between the downwards and upwards step. Note that maxt f (t) upwards and downwards steps, respectively, are not involved in down-up pairs. We may consider them as down-up pairs of infinite width. The cost of g obviously consists of the following summands: C times the number of upwards steps, D times the number of downwards steps, and the area bounded by the graph of g and the time axis. (Since the costs of busy threads must be paid anyhow, we may replace the last term with the area between the graphs of g and f .

Rn . So Lemma 2 yields n − 1 algebraic equations in n − 1 variables tk , k < n. We illustrate the application in case n = 2: √ Proposition 1. 81. Proof. By Lemma 2, r1 = 1 + 1/2t1 and r2 = 1 + (t1 + 1)/2. Thus t21 + t1 − 1 = 0. ✷ Denominators n > 2 lead to higher-order algebraic equations that may be solved numerically. 75, etc. It is important to estimate the competitive ratio for fixed n. Due to the following result, some n between 5 and 10 should be satisfactory in practice: Theorem 4. e/(e − 1) + 1/2n − 1/n2 < r < e/(e − 1) + 1/2n.

Suppose the sorted list of the elements of the set is divided into 2c blocks of size roughly n/2c each. Then the information stored with each element is precisely its rank within its block. e. the first element of the i-th block), for 1 ≤ i ≤ 2c . Given an element, the membership proceeds as in the case of our modified FKS strategy (as mentioned in the last section). Once an element is found, the block to which it belongs (in the sorted order) can be found by doing a binary search (using c steps) on the first elements of each block stored in the separate 22 V.

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