Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993
Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Target-Oriented Branch and Bound Method for Global Optimization
Journal of Global Optimization
A fast algorithm for the maximum clique problem
Discrete Applied Mathematics - Sixth Twente Workshop on Graphs and Combinatorial Optimization
A Branch and Bound Algorithm for the Stability Number of a Sparse Graph
INFORMS Journal on Computing
Exploiting semidefinite relaxations in constraint programming
Computers and Operations Research
An Efficient Branch-and-bound Algorithm for Finding a Maximum Clique with Computational Experiments
Journal of Global Optimization
The worst-case time complexity for generating all maximal cliques and computational experiments
Theoretical Computer Science - Computing and combinatorics
An efficient branch-and-bound algorithm for finding a maximum clique
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
An algorithm for finding a maximum clique in a graph
Operations Research Letters
Relaxed approximate coloring in exact maximum clique search
Computers and Operations Research
SQBC: An efficient subgraph matching method over large and dense graphs
Information Sciences: an International Journal
Improvements to MCS algorithm for the maximum clique problem
Journal of Combinatorial Optimization
Speeding up branch and bound algorithms for solving the maximum clique problem
Journal of Global Optimization
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This paper proposes new approximate coloring and other related techniques which markedly improve the run time of the branch-and-bound algorithm MCR (J. Global Optim., 37, 95–111, 2007), previously shown to be the fastest maximum-clique-finding algorithm for a large number of graphs. The algorithm obtained by introducing these new techniques in MCR is named MCS. It is shown that MCS is successful in reducing the search space quite efficiently with low overhead. Consequently, it is shown by extensive computational experiments that MCS is remarkably faster than MCR and other existing algorithms. It is faster than the other algorithms by an order of magnitude for several graphs. In particular, it is faster than MCR for difficult graphs of very high density and for very large and sparse graphs, even though MCS is not designed for any particular type of graphs. MCS can be faster than MCR by a factor of more than 100,000 for some extremely dense random graphs.