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Spectral bounds for graph partitioning with prescribed partition sizes.

Authors :
Anjos, Miguel F.
Neto, José
Source :
Discrete Applied Mathematics. Sep2019, Vol. 269, p200-210. 11p.
Publication Year :
2019

Abstract

Given an undirected edge weighted graph, the graph partitioning problem consists in determining a partition of the node set of the graph into subsets of prescribed sizes, so as to maximize the sum of the weights of the edges having both endpoints in the same subset. We introduce a new class of bounds for this problem relying on the full spectral information of the weighted adjacency matrix A. The expression of these bounds involves the eigenvalues and particular geometrical parameters defined using the eigenvectors of A. A connection is established between these parameters and the maximum cut problem. We report computational results showing that the new bounds compare favorably with previous bounds in the literature. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
0166218X
Volume :
269
Database :
Academic Search Index
Journal :
Discrete Applied Mathematics
Publication Type :
Academic Journal
Accession number :
139008646
Full Text :
https://doi.org/10.1016/j.dam.2019.06.007