Minimum Cut Supertree

The Minimum Cut Supertree algorithm, described in "A supertree method for rooted trees",Semple, C. and Steel, M., Discrete Applied Mathematics 105, 147-158, (2000), is a graph-based supertree method that allows to handle conflicting input trees. The algorithm has the following desireable properties(taken from "A supertree method for rooted trees"):
(1) The method has a polynomial time algorithm. 
(2) The method preserves nestings and binary subtrees that are shared by all of the input trees. 
(3)In case the input trees are compatible, the output tree displays each of the input trees. 
(4)The method satis es two natural symmetry requirements. In particular, (1) the output tree is independent of the order in which the input trees are listed and (2) if we rename all the leaves, and then apply our method to the new set of input trees, the output tree is simply the original output tree, but with the leaves renamed as before. 
(5)The method extends naturally to allow the input trees to be weighted