The Use of an Exact Algorithm within a Tabu Search Maximum Clique Algorithm

Derek H. Smith, Roberto Montemanni, Stephanie Perkins
2020 Algorithms  
Let G=(V,E) be an undirected graph with vertex set V and edge set E. A clique C of G is a subset of the vertices of V with every pair of vertices of C adjacent. A maximum clique is a clique with the maximum number of vertices. A tabu search algorithm for the maximum clique problem that uses an exact algorithm on subproblems is presented. The exact algorithm uses a graph coloring upper bound for pruning, and the best such algorithm to use in this context is considered. The final tabu search
more » ... ithm successfully finds the optimal or best known solution for all standard benchmarks considered. It is compared with a state-of-the-art algorithm that does not use exact search. It is slower to find the known optimal solution for most instances but is faster for five instances and finds a larger clique for two instances.
doi:10.3390/a13100253 fatcat:7panffvgengwnoq4votm6wwkvu