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...

Full description

Saved in:
Bibliographic Details
Published inSIAM journal on discrete mathematics Vol. 28; no. 1; pp. 342 - 371
Main Authors Banderier, Cyril, Hwang, Hsien-Kuei, Ravelomanana, Vlady, Zacharovas, Vytas
Format Journal Article
LanguageEnglish
Published 01.01.2014
Subjects
Algebra
Algorithms
Asymptotic properties
Constraining
Cost engineering
Graphs
Mathematical models
Search algorithms
Online AccessGet full text

Cover

More Information
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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0895-4801
1095-7146
DOI:10.1137/130916357