A1 Refereed original research article in a scientific journal
Finite metrics in switching classes
Authors: Ehrenfeucht A, Harju T, Rozenberg G
Publisher: ELSEVIER SCIENCE BV
Publication year: 2007
Journal:: Discrete Applied Mathematics
Journal name in source: DISCRETE APPLIED MATHEMATICS
Journal acronym: DISCRETE APPL MATH
Volume: 155
Issue: 1
First page : 68
Last page: 73
Number of pages: 6
ISSN: 0166-218X
DOI: https://doi.org/10.1016/j.dam.2006.04.041
Abstract
Lt g: D x D -> R be a symmetric function on a finite set D satisfying g(x, x) = 0 for all X E D. A switch g(n) of g w.r.t. a local valuation sigma: D -> R is defined by g(a)(x, y) = sigma(x) + g(x, y) + sigma(y) for x not equal y and g(sigma)(x, x) = 0 for all x. We show that every symmetric function g has a unique minimal semimetric switch, and, moreover, there is a switch of g that is isometric to a finite Manhattan metric. Also, for each metric on D, we associate an extension metric on the set of all nonempty subsets of D, and we show that this extended metric inherits the switching classes on D. (c) 2006 Elsevier B.V. All rights reserved.
Lt g: D x D -> R be a symmetric function on a finite set D satisfying g(x, x) = 0 for all X E D. A switch g(n) of g w.r.t. a local valuation sigma: D -> R is defined by g(a)(x, y) = sigma(x) + g(x, y) + sigma(y) for x not equal y and g(sigma)(x, x) = 0 for all x. We show that every symmetric function g has a unique minimal semimetric switch, and, moreover, there is a switch of g that is isometric to a finite Manhattan metric. Also, for each metric on D, we associate an extension metric on the set of all nonempty subsets of D, and we show that this extended metric inherits the switching classes on D. (c) 2006 Elsevier B.V. All rights reserved.
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