Finite metrics in switching classes
type: Item
instance of: scholarly article
title: Finite metrics in switching classes
zbMATH Open document ID: 1105.54013
author: Andrzej Ehrenfeucht
author: Tero Harju
author: Grzegorz Rozenberg
published in: Discrete Applied Mathematics
publication date: 2007-01-09T00:00:00Z
review text: Let \(D\) be a finite set, \(\sigma: D\to{\mathbb R}\) any function, and \(g:D\times D\to {\mathbb R}\) a function satisfying the conditions \(g(x,x)=0\) and \(g(x,y)=g(y,x)\). The authors introduce the function \(g^\sigma\) by the equalities \(g^\sigma(x,x)=0\) and \(g^\sigma(x,y)=\sigma(x)+g(x,y)+\sigma(y)\) if \(x\neq y\). The authors fix \(g\) and consider the set of all possible \(g^\sigma\), denoted by \([g]\). The paper is devoted to the structure of subsets of \([g]\) consisting of metrics, semimetrics, and \(L^1\)-embeddable semimetrics (cut semimetrics).
Mathematics Subject Classification ID: 54E25
Mathematics Subject Classification ID: 05C99
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 5082757
zbMATH Keywords: finite metric space
zbMATH Keywords: triangle inequality
zbMATH Keywords: switching class
zbMATH Keywords: Manhattan metric
zbMATH Keywords: semimetric
reviewed by: Mikhail Ostrovskii
MaRDI profile type: Publication
full work available at URL: j.dam.2006.04.041
OpenAlex ID: W2127648343
cites work: Q3954346
cites work: The cut cone,L1 embeddability, complexity, and multicommodity flows
cites work: Geometry of cuts and metrics
cites work: Q4492680
cites work: Theory of 2-structures. I: Clans, basic subclasses, and morphisms
cites work: Dynamic labeled 2-structures
cites work: Q3757929
cites work: Metrics and undirected cuts
cites work: Q4549227
cites work: Q5513521
cites work: Q4121914
cites work: Q3931443
DOI: 10.1016/J.DAM.2006.04.041
description: scientific article; zbMATH DE number 5082757