Abstract

this paper, it is shown how to take advantage of the properties of these models to approximately solve the maximum clique problem, a well-known intractable optimization problem which has practical applications in various fields. The approach is based on a result by Motzkin and Straus which naturally leads to formulate the problem in a manner that is readily mapped onto a relaxation labeling network. Extensive simulations have demonstrated the validity of the proposed model, both in terms of quality of solutions and speed. Maximum clique problem, relaxation labeling processes, neural networks, optimization. 1 INTRODUCTION

Citations

1055	Combinatorial Optimization: Algorithms and Complexity - Papadimitriou, Steiglitz - 1982
731	Computer Vision - Ballard, Brown
436	Neural computation of decisions in optimization problems - Hopfield, Tank
289	Scene labeling by relaxation operations - Rosenfeld, Hummel, et al. - 1976
194	Probalistic interpretation of feedforward classification network outputs, with relationships to statistical pattern recognition - Bridle - 1990
175	Approximating clique is almost NP-complete - Feige, Goldwasser, et al. - 1991
173	An inequality with applications to statistical estimation for probabilistic functions of a Markov process and to models for ecology - Baum, Eagon - 1967
160	An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition - Levinson, Rabiner, et al. - 1983
136	A new method for mapping optimization problems onto neural networks - Peterson, Söderberg - 1989
112	Mathematical population genetics - Ewens - 1979
99	Maxima for graphs and a new proof of a theorem of Turan, Canad - Motzkin, Straus - 1965
80	The maximum Clique problem - Pardalos, Xue - 1994
77	Optimal perceptual inference - Hinton, Sejnowksi - 1983
71	Kerbosch J: Finding all cliques of an undirected graph - Bron - 1973
70	Maximum likelihood competitive learning - Nowlan - 1990
68	An exact algorithm for the maximum clique problem - Carraghan, Pardalos - 1990
39	Growth transformations for functions on manifolds - Baum, Snell - 1968
37	Two stages of curve detection suggest two styles of visual computation - Zucker, Dobbins, et al. - 1989
34	Continuous characterization of the maximum clique problem - Gibbons, Hearn, et al. - 1997
33	Learning compatibility coefficients for relaxation labeling processes - Pelillo, Refice - 1994
29	Paradalos A Continuous Based Heuristic for the Maximum Clique Problem - Gibbons, Hearn, et al. - 1991
20	Approximating maximum clique with a Hopfield neural network - Jagota - 1995
19	Open questions about computation in cerebral cortex - Sejnowski - 1986
18	On the dynamics of relaxation labeling processes - Pelillo - 1994
18	A.: Feasible and infeasible maxima in a quadratic program for maximum clique - Pelillo, Jagota - 1995
17	R.: Approximately solving maximum clique using neural network and related heuristics - Jagota, Sanchis, et al. - 1996
13	A global optimization approach for solving the maximum clique problem - Pardalos, Philips - 1990
9	A neural network model for finding a nearmaximum clique - Funabiki, Takefuji, et al. - 1992
8	A parallel computation network for the maximum clique problem - Lin, Lee - 1992
5	Applying the INN model to the max clique problem - Grossman
4	Comparative performance measure for neural networks solving optimization problems - Protzel - 1990
3	Neural Network Refinements and Extensions - Denker - 1986
3	Homogeneous nonnegative symmetric quadratic transformations - Blakley