Title | ||
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Solving clique covering in very large sparse random graphs by a technique based on k-fixed coloring tabu search |
Abstract | ||
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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. |
Year | DOI | Venue |
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2013 | 10.1007/978-3-642-37198-1_21 | EvoCOP |
Keywords | Field | DocType |
sparse graph,known result,direct use,k available label,large sparse random graph,k-fixed graph coloring,k-fixed coloring tabu search,large dense graph,inverse strategy,method tabucol-ccp,k-fixed variant,tabu search | Discrete mathematics,Complete coloring,Combinatorics,Fractional coloring,Clique graph,Chordal graph,Independent set,Greedy coloring,Mathematics,Graph coloring,Split graph | Conference |
Volume | ISSN | Citations |
7832 | 0302-9743 | 0 |
PageRank | References | Authors |
0.34 | 14 | 1 |
Name | Order | Citations | PageRank |
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David Chalupa | 1 | 24 | 6.84 |