Maximum Agreement Subtree (of 3 or More Trees)

Years and Authors of Summarized Original Work

1995; Farach, Przytycka, Thorup

Problem Definition

The maximum agreement subtree problem for k trees (k-MAST) is a generalization of a similar problem for two trees (MAST). Consider a tuple of k rooted leaf-labeled trees (T ₁, T ₂ … T _k ). Let A = { a ₁, a ₂, … a _n } be the set of leaf labels. Any subset B ⊆ A uniquely determines the so-called topological restriction T | B of the three T to B. Namely, T | B is the topological subtree of T spanned by all leaves labeled with elements from B and the lowest common ancestors of all pairs of these leaves. In particular, the ancestor relation in T | B is defined so that it agrees with the ancestor relation in T. A subset B of A such T ¹ | B, …, T ^k | B are isomorphic is called an agreement set.

Problem 1 (k-MAST).

INPUT: A tuple $\vec{T} = (T^{1},\ldots, T^{k})$ of leaf-labeled trees, with a common set of labels A = { a ₁, …, a _n }, such that for each tree T ⁱthere exists one-to-one mapping...