New heuristics on Rooted Triplet Consistency ∗

Rooted triplets are becoming one of the important types of input for reconstructing 1 rooted phylogenies. A rooted triplet is a phylogenetic tree on three leaves and shows the 2 evolutionary relationship of the corresponding three species. In this paper, we investigate the 3 problem of inferring the maximum consensus evolutionary tree from a set of rooted triplets. 4 The mentioned problem is known to be APX-hard. We present two new heuristic algorithms. 5 For a given set of m triplets on n species, the FastTree algorithm runs in O(m + α(n)n) 6 time, where α(n) is functional inverse of Ackermann’s function. This is faster than any 7 other previously known algorithms, although, the outcome is less satisfactory. The BPMTR 8 algorithm runs in O(mn) time and in average performs better than any other previously 9 known algorithms for this problem. 10