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The maximum edge-weight clique problem is to find a clique whose sum ofedge-weight is the maximum for a given edge-weighted undirected graph. Theproblem is NP-hard and some branch-and-bound algorithms have been proposed. Inthis paper, we propose a new exact algorithm based on branch-and-bound. Itassigns edge-weights to vertices and calculates upper bounds using vertexcoloring. By some computational experiments, we confirmed our algorithm isfaster than previous algorithms.

A Maximum Edge-Weight Clique Extraction Algorithm Based on Branch-and-Bound