Résumé
We consider the following problem: given a forest of gene family trees on a set of genomes, find a first speciation which splits these genomes into two subsets and minimizes the number of gene duplications that happened before this speciation. We call this problem the Minimum Duplication Bipartition Problem. Using a generalization of the Minimum Edge-Cut Problem, known as Submodular Function Minimization, we propose a polynomial time and space 2-approximation algorithm for the Minimum Duplication Bipartition Problem. We illustrate the potential of this algorithm on both synthetic and real data.