Graph partitioning and continuous quadratic programming

Graph partitioning and continuous quadratic programming

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Article ID: iaor20003064
Country: United States
Volume: 12
Issue: 4
Start Page Number: 500
End Page Number: 523
Publication Date: Oct 1999
Journal: SIAM Journal on Discrete Mathematics
Authors: ,
Keywords: graphs
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.

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