  An evolutionary tree (phylogenetic tree) is a binary, rooted, unordered tree
that models the evolutionary history of currently living species in which
leaves are labeled by species. In this paper, we investigate the problem of
finding the maximum consensus evolutionary tree from a set of given rooted
triplets. A rooted triplet is a phylogenetic tree on three leaves and shows the
evolutionary relationship of the corresponding three species. The mentioned
problem is known to be APX-hard. We present two new heuristic algorithms. For a
given set of m triplets on n species, the FastTree algorithm runs in O(mn^2)
which is faster than any other previously known algorithms, although, the
outcome is less satisfactory. The BPMTR algorithm runs in O(mn^3) and in
average performs better than any other previously known approximation
algorithms for this problem.
