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The gene-duplication problem is to infer a species supertree from gene trees that are confounded by complex histories of gene duplications. This problem is NP-complete and thus requires efficient and effective heuristics. Existing heuristics perform a stepwise search of the tree space, where each step is guided by an exact solution to an instance of a local search problem. We improve on the time complexity of the local search problem by a factor of n2/logn, where n is the size of the resulting species supertree. Typically, several thousand instances of the local search problem are solved throughout a stepwise heuristic search. Hence, our improvement makes the gene-duplication problem much more tractable for large-scale phylogenetic analyses.