Integer point sets minimizing average pairwise L1 distance: What is the optimal shape of a town?

  • An n-town, n[is an element of]N , is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings along the axis-parallel street grid, then an n-town has optimal shape if the sum of all pairwise Manhattan distances is minimized. This problem has been studied for cities, i.e., the limiting case of very large n. For cities, it is known that the optimal shape can be described by a differential equation, for which no closed-form solution is known. We show that optimal n-towns can be computed in O(n[superscript 7.5]) time. This is also practically useful, as it allows us to compute optimal solutions up to n=80.

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Metadaten
Author:Erik D. Demaine, Sándor P. Fekete, Günter Rote, Nils Schweer, Daria Schymura, Mariano Zelke
URN:urn:nbn:de:hebis:30:3-259160
URL:http://hdl.handle.net/1721.1/62244
ISSN:0925-7721
Parent Title (English):Preprint zu: Computational geometry
Publisher:Elsevier B.V.
Place of publication:Amsterdam
Document Type:Preprint
Language:English
Year of Completion:2010
Year of first Publication:2010
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2013/06/14
Tag:Manhattan distance; average pairwise distance; dynamic programming; integer points
Volume:44
Issue:2
Page Number:13
First Page:82
Last Page:94
Note:
Terms of Use: Creative Commons Attribution-Noncommercial-Share Alike 3.0
Note:
Special issue of selected papers from the 21st Annual Canadian Conference on Computational Geometry. Citation: Demaine, Erik D. et al. “Integer Point Sets Minimizing Average Pairwise L1 Distance: What Is the Optimal Shape of a Town?” Computational Geometry 44.2 (2011) : 82-94.
HeBIS-PPN:34937418X
Institutes:Informatik und Mathematik / Informatik
Dewey Decimal Classification:0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - Namensnennung-Keine kommerzielle Nutzung-Weitergabe unter gleichen Bedingungen

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