Computer Laboratory Home Page Search A-Z Directory Help
University of Cambridge Home Logic and Semantics Seminar
14th August, 1998: Mike Steel
Computer Laboratory > Research > TSG > Logic and Semantics Seminar > 14th August, 1998: Mike Steel

Speaker: Mike Steel, University of Canterbury, Christchurch, New Zealand
Title: Reconstruction of X-Trees from Subtrees
Time: 14th August, 1998, 14:00
Abstract:

An X-tree is a finite tree T = (V,E), together with a map φ: X → V for which degT(v) ≤ 2 ⇒ v ∈&phi(X). Such trees are equivalent to `pairwise compatible' system of bipartitions of X and are widely used in classification, particularly in biology, but also in linguistics, philology etc.

In such applications we are often given a list T = { T1, ..., Tk } where Ti is an Xi-tree, for a (small) subset Xi of X, and we wish to determine if these trees can be consistently combined into one or more unknown `parent' X-trees. This tree reconstruction problem is closely related to another which takes as its input a collection of partitions of subsets of X.

We will discuss some of the resulting combinatorial and computational features of this problem. In particular we consider the class of all possible `inference rules' for enlarging any consistent collection of trees. We show that (as conjectured) this class is infinite, but under certain restrictions a small finite subset always suffices to reconstruct a tree. We also consider the question of whether or not this system of inference rules suffices to determine the consistency of T.