Branch-and-bound approaches to standard quadratic optimization problems
Journal of Global Optimization
A Complementary Pivoting Approach to Graph Matching
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Pattern Recognition Letters - Special issue: Graph-based representations in pattern recognition
Quartic Formulation of Standard Quadratic Optimization Problems
Journal of Global Optimization
A new trust region technique for the maximum weight clique problem
Discrete Applied Mathematics - Special issue: International symposium on combinatorial optimization CO'02
Simple ingredients leading to very efficient heuristics for the maximum clique problem
Journal of Heuristics
Complementary approaches for the computation of the independent number of a graph
MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
Self-adapting numerical software and automatic tuning of heuristics
ICCS'03 Proceedings of the 2003 international conference on Computational science
Graph polynomials, principal pivoting, and maximum independent sets
GbRPR'03 Proceedings of the 4th IAPR international conference on Graph based representations in pattern recognition
Survivable scheduled service provisioning in WDM optical networks with iterative routing
Optical Switching and Networking
The combinatorics of pivoting for the maximum weight clique
Operations Research Letters
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Given an undirected graph with positive weights on the vertices, the maximum weight clique problem (MWCP) is to find a subset of mutually adjacent vertices (i.e., a clique) having largest total weight. The problem is known to be NP-hard, even to approximate. Motivated by a recent quadratic programming formulation, which generalizes an earlier remarkable result of Motzkin and Straus, in this paper we propose a new framework for the MWCP based on the corresponding linear complementarity problem (LCP). We show that, generically, all stationary points of the MWCP quadratic program exhibit strict complementarity. Despite this regularity result, however, the LCP turns out to be inherently degenerate, and we find that Lemke's well-known pivoting method, equipped with standard degeneracy resolution strategies, yields unsatisfactory experimental results. We exploit the degeneracy inherent in the problem to develop a variant of Lemke's algorithm which incorporates a new and effective "look-ahead" pivot rule. The resulting algorithm is tested extensively on various instances of random as well as DIMACS benchmark graphs, and the results obtained show the effectiveness of our method.