Solving the maximum clique problem using a tabu search approach
Annals of Operations Research - Special issue on Tabu search
New methods to color the vertices of a graph
Communications of the ACM
Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993
Efficiently covering complex networks with cliques of similar vertices
Theoretical Computer Science - Complex networks
A survey of local search methods for graph coloring
Computers and Operations Research - Anniversary focused issue of computers & operations research on tabu search
Approximating the minimum clique cover and other hard problems in subtree filament graphs
Discrete Applied Mathematics
A graph coloring heuristic using partial solutions and a reactive tabu scheme
Computers and Operations Research
Data reduction and exact algorithms for clique cover
Journal of Experimental Algorithmics (JEA)
Computers and Operations Research
Note: Quantum annealing of the graph coloring problem
Discrete Optimization
On the efficiency of an order-based representation in the clique covering problem
Proceedings of the 14th annual conference on Genetic and evolutionary computation
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We propose a technique for solving the k-fixed variant of the clique covering problem (k-CCP), where the aim is to determine, whether a graph can be divided into at most k non-overlapping cliques. The approach is based on labeling of the vertices with k available labels and minimizing the number of non-adjacent pairs of vertices with the same label. This is an inverse strategy to k-fixed graph coloring, similar to a tabu search algorithm TabuCol. Thus, we call our method TabuCol-CCP. The technique allowed us to improve the best known results of specialized heuristics for CCP on very large sparse random graphs. Experiments also show a promise in scalability, since a large dense graph does not have to be stored. In addition, we show that Γ function, which is used to evaluate a solution from the neighborhood in graph coloring in $\mathcal{O}(1)$ time, can be used without modification to do the same in k-CCP. For sparse graphs, direct use of Γ allows a significant decrease in space complexity of TabuCol-CCP to $\mathcal{O}(|E|)$, with recalculation of fitness possible with small overhead in $\mathcal{O}(\log \deg(v))$ time, where deg(v) is the degree of the vertex, which is relabeled.