A short note on the tractability of constructing phylogenetic networks from clusters

In [2] it was proven that the Cass algorithm is a polynomial-time algorithm for constructing level<=2 networks from clusters. Here we demonstrate, for each k>=0, a polynomial-time algorithm for constructing level-k phylogenetic networks from clusters. Unlike Cass the algorithm scheme given here is only of theoretical interest. It does, however, strengthen the hope that efficient polynomial-time algorithms (and perhaps fixed parameter tractable algorithms) exist for this problem.