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A fast algorithm for the maximum clique problem Export

by: Patric R. östergård
Discrete Applied Mathematics, Vol. 120, No. 1-3. (15 August 2002), pp. 197-207.

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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.


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