The shoelace problem
type: Item
instance of: scholarly article
title: The shoelace problem
zbMATH Open document ID: 0834.90132
DOI: 10.1007/BF03024786
author: John H. Halton
published in: The Mathematical Intelligencer
publication date: 1996-03-10T00:00:00Z
review text: In a number of discussions of how shoes should be laced, it became apparent that no one seemed to have the definitive answer. Shoes were laced and relaced, passions flared, and shoes were even thrown\dots. The author decided that an appeal to mathematics was indicated. This problem is a restriction of the Traveling Salesman Problem. We are given a set of \(2(n+ 1)\) points (the lace-holes or eyelets) arranged in a bi-partite lattice. The problem is to find the shortest path passing through every eyelet just once, in such a way that the points of the `right' and `left' holes alternates. The author compares three `popular' lacing strategies and proved the minimality of the ordinary zig-zag lacing.
Mathematics Subject Classification ID: 90C35
Mathematics Subject Classification ID: 00A08
zbMATH DE Number: 821756
zbMATH Keywords: traveling salesman
zbMATH Keywords: shortest path
zbMATH Keywords: zig-zag lacing
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf03024786
OpenAlex ID: W4252024732
description: scientific article; zbMATH DE number 821756