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Open AccessArticle

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

1
School of Computing and Mathematics, University of South Wales, Pontypridd, Cardiff CF37 1DL, UK
2
Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Via Amendola 2 (Pad. Morselli), 42122 Modena MO, Italy
*
Author to whom correspondence should be addressed.
Algorithms 2020, 13(10), 253; https://doi.org/10.3390/a13100253
Received: 25 August 2020 / Revised: 21 September 2020 / Accepted: 22 September 2020 / Published: 4 October 2020
(This article belongs to the Special Issue Algorithms for Graphs and Networks)
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 algorithm 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. View Full-Text
Keywords: combinatorial optimization; maximum clique; hybrid algorithm; tabu search; benchmarks combinatorial optimization; maximum clique; hybrid algorithm; tabu search; benchmarks
MDPI and ACS Style

Smith, D.H.; Montemanni, R.; Perkins, S. The Use of an Exact Algorithm within a Tabu Search Maximum Clique Algorithm. Algorithms 2020, 13, 253.

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