[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
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