Quasi-median hulls in Hamming space are Steiner hulls

Authors:
Hans-Jürgen Bandelt;Arne Röhl
Affiliations:
Department of Mathematics, University of Hamburg, Bundesstr. 55, 20146 Hamburg, Germany;Department of Mathematics, University of Hamburg, Bundesstr. 55, 20146 Hamburg, Germany
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 5
Cited 1

Quasi-median graphs and algebras

Journal of Graph Theory
Algorithms on strings, trees, and sequences: computer science and computational biology

Algorithms on strings, trees, and sequences: computer science and computational biology
Sufficient Conditions for Two Tree Reconstruction Techniques to Succeed on Sufficiently Long Sequences

SIAM Journal on Discrete Mathematics
Quasi-median graphs from sets of partitions

Discrete Applied Mathematics
Invited Presentation: Median Hulls as Steiner Hulls in Rectilinear and Molecular Sequence Spaces

WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science

Visualization of quasi-median networks

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

A Hamming space @L^n consists of all sequences of length n over an alphabet @L and is endowed with the Hamming distance. In particular, any set of aligned DNA sequences of fixed length constitutes a subspace of a Hamming space with respect to mismatch distance. The quasi-median operation returns for any three sequences u,v,w the sequence which in each coordinate attains either the majority coordinate from u,v,w or else (in the case of a tie) the coordinate of the first entry, u; for a subset of @L^n the iterative application of this operation stabilizes in its quasi-median hull. We show that for every finite tree interconnecting a given subset X of @L^n there exists a shortest realization within @L^n for which all interior nodes belong to the quasi-median hull of X. Hence the quasi-median hull serves as a Steiner hull for the Steiner problem in Hamming space.