Comparisons of Energy-Descent Optimization Algorithms for Maximum Clique Problems


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A    No.4    pp.452-460
Publication Date: 1996/04/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
maximum clique,  NP-complete,  neural network,  algorithm,  energy-descent opimization,  

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A clique of a graph G(V,E) is a subset of V such that every pair of vertices is connected by an edge in E. Finding a maximum clique of an arbitrary graph is a well-known NP-complete problem. Recently, several polynomial time energy-descent optimization algorithms have been proposed for approximating the maximum clique problem, where they seek a solution by minimizing the energy function representing the constraints and the goal function. In this paper, we propose the binary neural network as an efficient synchronous energy-descent optimization algorithm. Through two types of random graphs, we compare the performance of four promising energy-descent optimization algorithms. The simulation results show that RaCLIQUE, the modified Boltzmann machine algorithm, is the best asynchronous algorithm for random graphs, while the binary neural network is the best one for k random cliques graphs.