FlipCut Supertrees: Towards Matrix Representation Accuracy in Polynomial Time

In computational phylogenetics, supertree methods provide a way to reconstruct larger clades of the Tree of Life. The supertree problem can be formalized in different ways, to cope with contradictory information in the input. In particular, there exist methods based on encoding the input trees in a matrix, and methods based on finding minimum cuts in some graph. Matrix representation methods compute supertrees of superior quality, but the underlying optimization problems are computationally hard. In contrast, graph-based methods have polynomial running time, but supertrees are inferior in quality. In this paper, we present a novel approach for the computation of supertrees called FlipCut supertree. Our method combines the computation of minimum cuts from graph-based methods with a matrix representation method, namely Minimum Flip Supertrees. Here, the input trees are encoded in a 0/1/?-matrix. We present a heuristic to search for a minimum set of 0/1-flips such that the resulting matrix admits a directed perfect phylogeny. We then extend our approach by using edge weights to weight the columns of the 0/1/?-matrix. In our evaluation, we show that our method is extremely swift in practice, and orders of magnitude faster than the runner up. Concerning supertree quality, our method is sometimes on par with the gold standard Matrix Representation with Parsimony.