Dual quadratic estimates in polynomial and boolean programming
Annals of Operations Research
Parameterized circuit complexity and the W hierarchy
Theoretical Computer Science
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
Vertex Cover: Further Observations and Further Improvements
WG '99 Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science
Simple and Fast: Improving a Branch-And-Bound Algorithm for Maximum Clique
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A new algorithm for the maximum-weight clique problem
Nordic Journal of Computing
A Parallel FPT Application For Clusters
CCGRID '03 Proceedings of the 3st International Symposium on Cluster Computing and the Grid
Fast algorithms for vertex packing and related problems
Fast algorithms for vertex packing and related problems
Solving large FPT problems on coarse-grained parallel machines
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
An algorithm for finding a maximum clique in a graph
Operations Research Letters
Parameterized Complexity
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We describe an improved algorithm for solving the Maximum Clique problem in a graph using a novel sampling technique combined with a parameterized k-vertex cover algorithm. Experimental research shows that this approach greatly improves the execution time of the search, and in addition, provides intermediate results during computation. We also examine a very effective heuristic for finding a large clique that combines our sampling approach with fast independent set approximation. In experiments using the DIMACS benchmark, the heuristical approach established new lower bounds for four instances and provides the first optimal solution for an instance unsolved until now. The heuristic competitively matched the accuracy of the current best exact algorithm in terms of correct solutions, while requiring a fraction of the run time. Ideally such an approach could be beneficial as a preprocessing step to any exact algorithm, providing an accurate lower bound on the maximum clique, in very short time.