Order distances and split systems

Moulton, Vincent ORCID: https://orcid.org/0000-0001-9371-6435 and Spillner, Andreas (2022) Order distances and split systems. Order, 39 (2). 291–308. ISSN 0167-8094

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Given a pairwise distance D on the elements in a finite set X, the order distanceΔ(D) on X is defined by first associating a total preorder ≼ x on X to each x ∈X based on D, and then quantifying the pairwise disagreement between these total preorders. The order distance can be useful in relational analyses because using Δ(D) instead of D may make such analyses less sensitive to small variations in D. Relatively little is known about properties of Δ(D) for general distances D. Indeed, nearly all previous work has focused on understanding the order distance of a treelike distance, that is, a distance that arises as the shortest path distances in a tree with non-negative edge weights and X mapped into its vertex set. In this paper we study the order distance Δ(D) for distances D that can be decomposed into sums of simpler distances called split-distances. Such distances D generalize treelike distances, and have applications in areas such as classification theory and phylogenetics.

Item Type: Article
Uncontrolled Keywords: circular split system,flat split system,kalmanson distance,order distance,total preorder,treelike distance,algebra and number theory,geometry and topology,computational theory and mathematics ,/dk/atira/pure/subjectarea/asjc/2600/2602
Faculty \ School: Faculty of Science > School of Computing Sciences
UEA Research Groups: Faculty of Science > Research Groups > Computational Biology
Faculty of Science > Research Groups > Norwich Epidemiology Centre
Faculty of Medicine and Health Sciences > Research Groups > Norwich Epidemiology Centre
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Depositing User: LivePure Connector
Date Deposited: 11 Sep 2021 00:17
Last Modified: 20 Apr 2023 22:35
URI: https://ueaeprints.uea.ac.uk/id/eprint/81387
DOI: 10.1007/s11083-021-09579-y

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