Minimally distant sets of lattice points
type: Item
instance of: scholarly article
title: Minimally distant sets of lattice points
zbMATH Open document ID: 0777.05055
author: Daniel J. Kleitman
author: Leonard J. Schulman
published in: European Journal of Combinatorics
publication date: 1993-08-25T00:00:00Z
review text: In this paper, authors consider the problem of finding two sets of given cardinalities \(x\) and \(y\) in certain grid graphs, to minimize the maximum distance between two nodes respectively in the two sets. This minimax distance is denoted by \(D(x,y)\). For grids that are a product of chains of even edge length, and for the \(n\)-cube, the problem is solved completely. The answer in these cases is that both sets are initial segments of some ordering of vertices. An open question proposed in the end of this paper is as follows: For which chain products do orderings of the vertices exist such that initial segments minimize \(D(x,x)\), for all \(x\)?
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 370661
zbMATH Keywords: lattice points
zbMATH Keywords: grid graphs
zbMATH Keywords: minimax distance
reviewed by: Du Ding-Zhu
MaRDI profile type: Publication
full work available at URL: eujc.1993.1026
OpenAlex ID: W1976597334
DOI: 10.1006/EUJC.1993.1026
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description: scientific article; zbMATH DE number 370661