Analysis in distribution of two randomized algorithms for finding the maximum in a broadcast communication model |
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Authors: | Wei-Mei Chen Hsien-Kuei Hwang |
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Affiliation: | a Department of Applied Mathematics, Tatung University, Taipei 104, Taiwan;b Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan |
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Abstract: | The limit laws of three cost measures are derived of two algorithms for finding the maximum in a single-channel broadcast communication model. Both algorithms use coin flips and comparisons. Besides the ubiquitous normal limit law, the Dickman distribution also appears in a natural way. The method of proof proceeds along the line via the method of moments and the “asymptotic transfers,” which roughly bridges the asymptotics of the “conquering cost of the subproblems” and that of the total cost. Such a general approach has proved very fruitful for a number of problems in the analysis of recursive algorithms. |
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Keywords: | Broadcast communication model Analysis in distribution Asymptotic normality Dickman distribution Method of moment Binomial recurrence |
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