NDLI: Graph Partitioning and Continuous Quadratic Programming

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Graph Partitioning and Continuous Quadratic Programming

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Hager, William W. Krylyuk, Yaroslav
Copyright Year	1999
Abstract	A continuous quadratic programming formulation is given for min-cut graph partitioning problems. In these problems, we partition the vertices of a graph into a collection of disjoint sets satisfying specified size constraints, while minimizing the sum of weights of edges connecting vertices in different sets. An optimal solution is related to an eigenvector (Fiedler vector) corresponding to the second smallest eigenvalue of the graph's Laplacian. Necessary and sufficient conditions characterizing local minima of the quadratic program are given. The effect of diagonal perturbations on the number of local minimizers is investigated using a test problem from the literature.
Starting Page	500
Ending Page	523
Page Count	24
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480199335829
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	4
Volume Number	12
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	optimality conditions max-cut edge separators graph partitioning graph Laplacian Quadratic programming Combinatorial optimization quadratic programming Fiedler vector min-cut Programming involving graphs or networks
Content Type	Text
Resource Type	Article
Subject	Mathematics

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