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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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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: | |
| 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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