On the Maximal Error of Spectral Approximation of Graph Bisection

Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class of graphs, we prove that the standard spectral graph bisectio...

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Bibliographic Details
Published inarXiv.org
Main Authors Urschel, John C, Zikatanov, Ludmil T
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.12.2015
Subjects
Approximation
Graphs
Mathematical analysis
Mathematics - Numerical Analysis
Spectra
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Summary:Spectral graph bisections are a popular heuristic aimed at approximating the solution of the NP-complete graph bisection problem. This technique, however, does not always provide a robust tool for graph partitioning. Using a special class of graphs, we prove that the standard spectral graph bisection can produce bisections that are far from optimal. In particular, we show that the maximum error in the spectral approximation of the optimal bisection (partition sizes exactly equal) cut for such graphs is bounded below by a constant multiple of the order of the graph squared.
ISSN:2331-8422
DOI:10.48550/arxiv.1512.06325