One of evolutionary molecular biology fundamental issues is to discover genomic duplication events and their correspondence to the species tree. Such events can be reconstructed by clustering single gene duplications inferred by reconciling a set of gene trees with a species tree. Here we propose the first solutions to the genomic duplication problem in which every reconciliation with the minimal number of single gene duplications is allowed and the method of clustering called minimum episodes under the assumption that input gene trees are unrooted. We showed new theoretical properties of unrooted reconciliation for the duplication cost and apply them to design several exact and heuristic algorithms for solving the problem. Our evaluation study on empirical dataset confirmed several genomic duplication events from the literature and demonstrate that algorithms can be successfully applied.
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