Constructing the maximum consensus tree from rooted triples

Abstract

We investigated the problem of constructing the maximum consensus tree from rooted triples. We showed the NP-hardness of the problem and developed exact and heuristic algorithms. The exact algorithm is based on the dynamic programming strategy . The heuristic algorithms were tested and their performances are shown by comparing with the optimal solutions. The experimental results show that the worst and average case relative error ratios are 1.214 and 1.075 respectively, which are much better than the previously best approximation ratio of the problem.