Diversities and the generalized circumradius

Bryant, David, Huber, Katharina T., Moulton, Vincent ORCID: https://orcid.org/0000-0001-9371-6435 and Tupper, Paul F. (2023) Diversities and the generalized circumradius. Discrete and Computational Geometry. ISSN 0179-5376 (In Press)

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Abstract

The generalized circumradius of a set of points A\subseteq R^d with respect to a convex body K equals the minimum value of \lambda\geq 0 such that a translate of  \lambda K contains A. Each choice of K gives a different function on the set of bounded subsets of R^d; we characterize which functions can arise in this way. Our characterization draws on the theory of diversities, a recently introduced generalization of metrics from functions on pairs to functions on finite subsets. We additionally investigate functions which arise by restricting the generalized circumradius to a finite subset of R^d. We obtain elegant characterizations in the case that K is a simplex or parallelotope.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Depositing User: LivePure Connector
Date Deposited: 16 Jan 2023 17:32
Last Modified: 16 Jan 2023 17:32
URI: https://ueaeprints.uea.ac.uk/id/eprint/90611
DOI:

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