Finding a maximum clique in an arbitrary graph
SIAM Journal on Computing
Computer Vision
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Computers and Intractability: A Guide to the Theory of NP-Completeness
Annealed replication: a new heuristic for the maximum clique problem
Discrete Applied Mathematics
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Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
Dynamic local search for the maximum clique problem
Journal of Artificial Intelligence Research
Approximating the maximum weight clique using replicator dynamics
IEEE Transactions on Neural Networks
Cooperating local search for the maximum clique problem
Journal of Heuristics
Breakout Local Search for maximum clique problems
Computers and Operations Research
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This paper extends the recently introduced Phased Local Search (PLS) algorithm to more difficult maximum clique problems and also adapts the algorithm to handle maximum vertex/edge weighted clique instances. PLS is a stochastic reactive dynamic local search algorithm that interleaves sub-algorithms which alternate between sequences of iterative improvement, during which suitable vertices are added to the current sub-graph, and plateau search, where vertices of the current sub-graph are swapped with vertices not contained in the current sub-graph. These sub-algorithms differ in firstly their vertex selection techniques in that selection can be solely based on randomly selecting a vertex, randomly selecting within highest vertex degree, or random selecting within vertex penalties that are dynamically adjusted during the search. Secondly, the perturbation mechanism used to overcome search stagnation differs between the sub-algorithms. PLS has no problem instance dependent parameters and achieves state-of-the-art performance for maximum clique and maximum vertex/edge weighted clique problems over a large range of the commonly used DIMACS benchmark instances.