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The maximum labelled clique problem is a variant of the maximum cliqueproblem where edges in the graph are given labels, and we are not allowed touse more than a certain number of distinct labels in a solution. We introduce anew branch-and-bound algorithm for the problem, and explain how it may beparallelised. We evaluate an implementation on a set of benchmark instances,and show that it is consistently faster than previously published results,sometimes by four or five orders of magnitude.

A Parallel Branch and Bound Algorithm for the Maximum Labelled Clique Problem