Article (Scientific journals)
Nonstandard n-distances based on certain geometric constructions
Kiss, Gergely; MARICHAL, Jean-Luc
2023In Beiträge zur Algebra und Geometrie, 64 (1), p. 107-126
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Keywords :
Metric geometry; n-distance; simplex inequality; Chebyshev ball; Euclidean minimal spanning tree; Euclidean Steiner tree; smallest enclosing ball
Abstract :
[en] The concept of n-distance was recently introduced to generalize the classical definition of distance to functions of n arguments. In this paper we investigate this concept through a number of examples based on certain geometrical constructions. In particular, our study shows to which extent the computation of the best constant associated with an n-distance may sometimes be difficult and tricky. It also reveals that two important graph theoretical concepts, namely the total length of the Euclidean Steiner tree and the total length of the minimal spanning tree constructed on n points, are instances of n-distances.
Disciplines :
Mathematics
Author, co-author :
Kiss, Gergely;  Alfred Renyi Institute of Mathematics, Hungarian Academy of Science
MARICHAL, Jean-Luc ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
External co-authors :
yes
Language :
English
Title :
Nonstandard n-distances based on certain geometric constructions
Publication date :
21 February 2023
Journal title :
Beiträge zur Algebra und Geometrie
ISSN :
0138-4821
eISSN :
2191-0383
Publisher :
Springer, Berlin, Germany
Volume :
64
Issue :
1
Pages :
107-126
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
Funders :
University of Luxembourg - UL
Available on ORBilu :
since 14 October 2021

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