Subtree distances, tight spans and diversities

Bryant, David, Huber, Katharina, Moulton, Vincent and Spillner, Andreas (2025) Subtree distances, tight spans and diversities. Topology and its Applications. ISSN 0166-8641 (In Press)

PDF (Arboreal_Diversities_submitted) - Accepted Version Restricted to Repository staff only until 31 December 2099. Available under License Creative Commons Attribution Non-commercial No Derivatives. Request a copy

Abstract

We characterize when a set of distances d(x, y) between elements in a set X have a subtree representation, a real tree T and a collection {Sx}x∈X of subtrees of T such that d(x, y) equals the length of the shortest path in T from a point in Sx to a point in Sy for all x, y ∈ X. The characterization was first established for finite X by Hirai (2006) using a tight span construction defined for distance spaces, metric spaces without the triangle inequality. To extend Hirai’s result beyond finite X we establish fundamental results of tight span theory for general distance spaces, including the surprising observation that the tight span of a distance space is hyperconvex. We apply the results to obtain the first characterization of when a diversity – a generalization of a metric space which assigns values to all finite subsets of X, not just to pairs – has a tight span which is tree-like

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Norwich Epidemiology Centre Faculty of Medicine and Health Sciences > Research Groups > Norwich Epidemiology Centre Faculty of Science > Research Groups > Computational Biology
Depositing User:	LivePure Connector
Date Deposited:	08 Aug 2025 14:30
Last Modified:	08 Aug 2025 14:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/100117
DOI:	issn:0166-8641

Actions (login required)

View Item