Graph Partitioning and Continuous Quadratic Programming

Authors:
William W. Hager;Yaroslav Krylyuk
Affiliations:
-;-
Venue:
SIAM Journal on Discrete Mathematics
Year:
1999

Citing 0
Cited 7

References

Sourcebook of parallel computing
The Gradient Projection Method with Exact Line Search

Journal of Global Optimization
Solving the quadratic trust-region subproblem in a low-memory BFGS framework

Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
A new k-graph partition algorithm for distributed P2P simulation systems

ICA3PP'07 Proceedings of the 7th international conference on Algorithms and architectures for parallel processing
Linear and quadratic programming approaches for the general graph partitioning problem

Journal of Global Optimization
An Affine-Scaling Interior-Point Method for Continuous Knapsack Constraints with Application to Support Vector Machines

SIAM Journal on Optimization
Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization

Journal of Global Optimization

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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.