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, 70 (4). 1862–1883. ISSN 0179-5376

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The generalized circumradius of a set of points A⊆ R d with respect to a convex body K equals the minimum value of λ≥ 0 such that a translate of λK 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
Additional Information: Funding Information: PT is supported by an NSERC (Canada) Discovery Grant. DB, KTH and VM thank the Royal Society for its support.
Uncontrolled Keywords: convex geometry,diversity,generalized minkowski spaces,generalized circumradius,metric geometry,theoretical computer science,geometry and topology,discrete mathematics and combinatorics,computational theory and mathematics ,/dk/atira/pure/subjectarea/asjc/2600/2614
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: 16 Jan 2023 17:32
Last Modified: 13 Dec 2023 01:54
URI: https://ueaeprints.uea.ac.uk/id/eprint/90611
DOI: 10.1007/s00454-023-00493-1


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