Covering a square by small perimeter rectangles
type: Item
instance of: scholarly article
title: Covering a square by small perimeter rectangles
zbMATH Open document ID: 0601.52009
DOI: 10.1007/BF02187679
published in: Discrete \& Computational Geometry
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/130977
review text: Given a partition of the unit square into n rectangles whose edges are parallel to the coordinate axes, we denote by p(n) the largest of their perimeters. The authors show that p(n) equals at least \(4(2m+1)/(n+m(m+1)),\) where m is the largest integer whose square does not exceed n: they define a linear program for p(n) and solve it by duality considerations, using the fact that the dual program only has three variables. An upper bound for p(n), as well as a discussion of several related questions, are included.
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52C17
Mathematics Subject Classification ID: 94A05
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 3969537
zbMATH Keywords: perimeter
zbMATH Keywords: partition
zbMATH Keywords: rectangles
zbMATH Keywords: linear program
zbMATH Keywords: dual program
author: Noga Alon
author: Daniel J. Kleitman
reviewed by: P. Mani-Levitska
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3969537