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Diversities and the Generalized Circumradius
The generalized circumradius of a set of points [Formula: see text] with respect to a convex body K equals the minimum value of [Formula: see text] such that a translate of [Formula: see text] contains A. Each choice of K gives a different function on the set of bounded subsets of [Formula: see text...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10676334/ https://www.ncbi.nlm.nih.gov/pubmed/38022897 http://dx.doi.org/10.1007/s00454-023-00493-1 |
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author | Bryant, David Huber, Katharina T. Moulton, Vincent Tupper, Paul F. |
author_facet | Bryant, David Huber, Katharina T. Moulton, Vincent Tupper, Paul F. |
author_sort | Bryant, David |
collection | PubMed |
description | The generalized circumradius of a set of points [Formula: see text] with respect to a convex body K equals the minimum value of [Formula: see text] such that a translate of [Formula: see text] contains A. Each choice of K gives a different function on the set of bounded subsets of [Formula: see text] ; 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 [Formula: see text] . We obtain elegant characterizations in the case that K is a simplex or parallelotope. |
format | Online Article Text |
id | pubmed-10676334 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-106763342023-04-13 Diversities and the Generalized Circumradius Bryant, David Huber, Katharina T. Moulton, Vincent Tupper, Paul F. Discrete Comput Geom Article The generalized circumradius of a set of points [Formula: see text] with respect to a convex body K equals the minimum value of [Formula: see text] such that a translate of [Formula: see text] contains A. Each choice of K gives a different function on the set of bounded subsets of [Formula: see text] ; 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 [Formula: see text] . We obtain elegant characterizations in the case that K is a simplex or parallelotope. Springer US 2023-04-13 2023 /pmc/articles/PMC10676334/ /pubmed/38022897 http://dx.doi.org/10.1007/s00454-023-00493-1 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Article Bryant, David Huber, Katharina T. Moulton, Vincent Tupper, Paul F. Diversities and the Generalized Circumradius |
title | Diversities and the Generalized Circumradius |
title_full | Diversities and the Generalized Circumradius |
title_fullStr | Diversities and the Generalized Circumradius |
title_full_unstemmed | Diversities and the Generalized Circumradius |
title_short | Diversities and the Generalized Circumradius |
title_sort | diversities and the generalized circumradius |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10676334/ https://www.ncbi.nlm.nih.gov/pubmed/38022897 http://dx.doi.org/10.1007/s00454-023-00493-1 |
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