A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
Scalable Parallel Algorithms for FPT Problems
Algorithmica
An Efficient Branch-and-bound Algorithm for Finding a Maximum Clique with Computational Experiments
Journal of Global Optimization
Parallel vertex cover: a case study in dynamic load balancing
AusPDC '11 Proceedings of the Ninth Australasian Symposium on Parallel and Distributed Computing - Volume 118
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The significance of graph coloring is considered in the context of reducing the running time of a parallel branch and bound algorithm to solve the maximum clique problem. The greedy color preprocessing algorithm produces an upper bound u on the color degree c of a vertex v. The color degree of a vertex is defined to be the chromatic number, γ, of the neighborhood subgraph of vertex v. The graph instance is reduced by removing any vertex v, such that u k, where k is the size of the largest known clique. The use of this graph coloring is extended and used in the interleaved preprocessing step during the branching phase of the algorithm. The basic techniques introduced can be extended to other problems such as minimum vertex cover and maximum independent set. Finally, results are presented from experiments using real biological data.