A new trust region technique for the maximum weight clique problem

Authors:
Stanislav Busygin
Affiliations:
Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL
Venue:
Discrete Applied Mathematics - Special issue: International symposium on combinatorial optimization CO'02
Year:
2006

Citing 11
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Abstract

A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of other stationary points of the program. We formulate and prove a condition when a Motzkin-Straus optimum coincides with such a point. The developed method has complexity O(n3), where n is the number of vertices of the graph. It was implemented in a publicly available software package QUALEX-MS.Computational experiments indicate that the algorithm is exact on small graphs and very efficient on the DIMACS benchmark graphs and various random maximum weight clique problem instances.