Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
421452 | Discrete Applied Mathematics | 2007 | 6 Pages |
Abstract
Let g:D×D→Rg:D×D→R be a symmetric function on a finite set D satisfying g(x,x)=0g(x,x)=0 for all x∈Dx∈D. A switch gσgσ of g w.r.t. a local valuation σ:D→Rσ:D→R is defined by gσ(x,y)=σ(x)+g(x,y)+σ(y)gσ(x,y)=σ(x)+g(x,y)+σ(y) for x≠yx≠y and gσ(x,x)=0gσ(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.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Andrzej Ehrenfeucht, Tero Harju, Grzegorz Rozenberg,