Diversities and the generalized circumradius

Bryant, David, Huber, Katharina T., Moulton, Vincent 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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Abstract

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
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	16 Jan 2023 17:32
Last Modified:	15 Jul 2025 20:33
URI:	https://ueaeprints.uea.ac.uk/id/eprint/90611
DOI:	10.1007/s00454-023-00493-1

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