A fast algorithm for the maximum clique problem

Authors:
Patric R. J. Östergård
Affiliations:
Department of Computer Science and Engineering, Helsinki University of Technology, P. O. Box 5400, 02015 HUT, Finland
Venue:
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Year:
2002

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Abstract

Given a graph, in the maximum clique problem, one desires to find the largest number of vertices, any two of which are adjacent. A branch-and-bound algorithm for the maximum clique problem--which is computationally equivalent to the maximum independent (stable) set problem--is presented with the vertex order taken from a coloring of the vertices and with a new pruning strategy. The algorithm performs successfully for many instances when applied to random graphs and DIMACS benchmark graphs.