Abstract
Graph coloring is one of the most studied NP-hard problems with a wide range of applications. In this work, the first solution-driven multilevel algorithm for this computationally challenging problem is investigated. Following the general idea of multilevel optimization, the proposed algorithm combines an original solution-driven coarsening procedure with an uncoarsening procedure as well as an effective refinement procedure. The algorithm is assessed on 47 popular DIMACS and COLOR benchmark graphs, and compared with 13 state-of-the-art coloring methods in the literature. We close one large graph (wap01a.col) by providing its chromatic number for the first time. Impacts of the key ingredients of the algorithm are also investigated.
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