The synthesis of two compatible rooted trees in a rooted supertree by an algorithm on sets

The tree compatibility problem is a problem arising in the theory of computational biology. For a species set S, the problem asks whether τ, a family of trees on S, is compatible, in the sense that there is a single tree T from which each tree of the family can be derived by a sequence of edge contractions. Steel (1992) demonstrated that this problem is NP-complete if τ is a family of unrooted trees. Polynomial time algorithms exist when τ is a finite family of rooted trees. In this paper, we present an algorithm for constructing a rooted tree from a set of constraints on subsets of a set of elements. We then apply this algorithm to synthesize a rooted supertree, compatible with two given rooted trees