The Steiner ratio of several discrete metric spaces
type: Item
instance of: scholarly article
title: The Steiner ratio of several discrete metric spaces
zbMATH Open document ID: 1017.05035
DOI: 10.1016/S0012-365X(02)00762-8
published in: Discrete Mathematics
publication date: 2003-03-16T00:00:00Z
review text: The author studies the greatest lower bound on the Steiner ratio \[ m(X,\rho)= \inf \left\{\frac{L(\text{SMT for }N)}{L(\text{MST for }N)}:\;N \text{ finite subset of }X,\text{ and }(X,\rho)\text{ metric space}\right\}, \] where SMT stands for Steiner minimal tree and MST for minimum spanning tree, and \(L\) is the length of the corresponding tree. He receives estimates and exact values for \(m(X,\rho)\) in several discrete spaces. Particularly, he determines the Steiner ratio for spaces of words and estimates the Steiner ratio for specific graphs.
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 1882190
zbMATH Keywords: Steiner ratio
zbMATH Keywords: metric space
zbMATH Keywords: Steiner minimal tree
zbMATH Keywords: minimum spanning tree
author: Dietmar Cieslik
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1882190