Constructing the Maximum Consensus Tree from Rooted Triples

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 and runs in O((m + n²)3ⁿ) time and O(2ⁿ) space. The heuristic algorithms run in polynomial time and their performances are tested and shown by comparing with the optimal solutions. In the tests, the worst and average relative error ratios are 1.200 and 1.072 respectively. We also implemented the two heuristic algorithms proposed by Gasieniec et al. The experimental result shows that our heuristic algorithm is better than theirs in most of the tests.