Regular Article: Trees, Taxonomy, and Strongly Compatible Multi-state Characters

Authors:
Andreas Dress;Vincent Moulton;Michael Steel
Affiliations:
FSPM Strukturbildungsprozesse, University of Bielefeld, Postfach 10 01 31, D-33501, Bielefeld, Germany;FSPM Strukturbildungsprozesse, University of Bielefeld, Postfach 10 01 31, D-33501, Bielefeld, Germany;Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
Venue:
Advances in Applied Mathematics
Year:
1997

Citing 0
Cited 8

The relation graph

Discrete Mathematics - Algebraic and topological methods in graph theory
Quasi-median graphs from sets of partitions

Discrete Applied Mathematics
Hyperbolic bridged graphs

European Journal of Combinatorics
Replacing cliques by stars in quasi-median graphs

Discrete Applied Mathematics
Compatible decompositions and block realizations of finite metrics

European Journal of Combinatorics
An algorithm for computing virtual cut points in finite metric spaces

COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Visualization of quasi-median networks

Discrete Applied Mathematics
Distance labeling in hyperbolic graphs

ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a family ofbinarycharacters defined on a setX, a problem arising in biological and linguistic classification is to decide whether there is a tree structure onXwhich is ''compatible'' with this family. A fundamental result from hierarchical clustering theory states that there exists a tree structure onXfor such a family if and only if any two of the characters arecompatible. In this paper, we prove a generalization of this result. Namely, we show that given a family ofmulti-statecharacters onXwhich we denote by @g, there exists a tree structure onX, called an (X,@g)-tree, which is ''compatible'' with @g if and only if any two of the characters arestrongly compatible. To prove this result, we introduce the concept ofblock systems, set theoretical structures which arise naturally from, amongst other things,block graphs, and the related concepts ofblock interval systemsand @D-systems.