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Graph partitioning and continuous quadratic programming (1999)
| Venue: | SIAM J. DISCRETE MATH |
| Citations: | 22 - 8 self |
BibTeX
@ARTICLE{Hager99graphpartitioning,
author = {William W. Hager and Yaroslav Krylyuk},
title = {Graph partitioning and continuous quadratic programming},
journal = {SIAM J. DISCRETE MATH},
year = {1999},
pages = {500--523}
}
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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.
Keyphrases
graph partitioning continuous quadratic programming diagonal perturbation local minimizers sufficient condition fiedler vector test problem different set optimal solution min-cut graph local minimum quadratic program continuous quadratic programming formulation graph laplacian size constraint disjoint set
