Analysis of an Exhaustive Search Algorithm in Random Graphs and the $nc\log n}$-Asymptotics
We analyze the cost used by a naive exhaustive search algorithm for finding a maximum independent set in random graphs under the usual $\mathscr{G}_{n,p}$-model where each possible edge appears independently with the same probability $p$. The expected cost turns out to be of the less common asymptot...
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Published in | SIAM journal on discrete mathematics Vol. 28; no. 1; pp. 342 - 371 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
01.01.2014
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Subjects | |
Online Access | Get full text |
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Summary: | We analyze the cost used by a naive exhaustive search algorithm for finding a maximum independent set in random graphs under the usual $\mathscr{G}_{n,p}$-model where each possible edge appears independently with the same probability $p$. The expected cost turns out to be of the less common asymptotic order $nc\log n}$, which we explore from several different perspectives. Also we collect many instances where such an order appears, from algorithmics to analysis, from probability to algebra. The limiting distribution of the cost required by the algorithm under a purely idealized random model is proved to be normal. The approach we develop is of some generality and is amenable for other graph algorithms. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0895-4801 1095-7146 |
DOI: | 10.1137/130916357 |