Reference : Nonstandard n-distances based on certain geometric constructions
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
Nonstandard n-distances based on certain geometric constructions
Kiss, Gergely [Alfred Renyi Institute of Mathematics, Hungarian Academy of Science]
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
In press
Beiträge zur Algebra und Geometrie
Yes (verified by ORBilu)
[en] Metric geometry ; n-distance ; simplex inequality ; Chebyshev ball ; Euclidean minimal spanning tree ; Euclidean Steiner tree ; smallest enclosing ball
[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.
University of Luxembourg - UL
Researchers ; Professionals ; Students

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