Improved Practical Algorithms for Rooted Subtree Prune and Regraft (rSPR) Distance and Hybridization Number

The problem of computing the rooted subtree prune and regraft (rSPR) distance of two phylogenetic trees is computationally hard and so is the problem of computing the hybridization number of two phylogenetic trees (denoted by Hybridization Number Computation [HNC]). Since they are important problems in phylogenetics, they have been studied extensively in the literature. Indeed, quite a number of exact or approximation algorithms have been designed and implemented for them. In this article, we design and implement several approximation algorithms for them and one exact algorithm for HNC. Our experimental results show that the resulting exact program is much faster (namely, more than 80 times faster for the easiest dataset used in the experiments) than the previous best and its superiority in speed becomes even more significant for more difficult instances. Moreover, the resulting approximation program's output has much better results than the previous bests; indeed, the outputs are always nearly optimal and often optimal. Of particular interest is the usage of the Monte Carlo tree search (MCTS) method in the design of our approximation algorithms. Our experimental results show that with MCTS, we can often solve HNC exactly within short time.