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dc.contributor.authorDemaine, Erik D.
dc.contributor.authorFekete, Sandor P.
dc.contributor.authorRote, Günter
dc.contributor.authorSchweer, Nils
dc.contributor.authorSchymura, Daria
dc.contributor.authorZelke, Mariano
dc.date.accessioned2011-04-19T20:58:44Z
dc.date.available2011-04-19T20:58:44Z
dc.date.issued2010-09
dc.date.submitted2009-11
dc.identifier.issn0925-7721
dc.identifier.urihttp://hdl.handle.net/1721.1/62244
dc.descriptionSpecial issue of selected papers from the 21st Annual Canadian Conference on Computational Geometryen_US
dc.description.abstractAn 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.en_US
dc.language.isoen_US
dc.publisherElsevier B.V.en_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.comgeo.2010.09.004en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alike 3.0en_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/en_US
dc.sourceMIT web domainen_US
dc.titleInteger point sets minimizing average pairwise L[subscript 1] distance: What is the optimal shape of a town?en_US
dc.title.alternativeInteger point sets minimizing average pairwise L1 distance: What is the optimal shape of a town?en_US
dc.typeArticleen_US
dc.identifier.citationDemaine, 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.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratoryen_US
dc.contributor.approverDemaine, Erik D.
dc.contributor.mitauthorDemaine, Erik D.
dc.relation.journalComputational Geometry: Theory and Applicationsen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/ConferencePaperen_US
dspace.orderedauthorsDemaine, Erik D.; Fekete, Sándor P.; Rote, Günter; Schweer, Nils; Schymura, Daria; Zelke, Marianoen
dc.identifier.orcidhttps://orcid.org/0000-0003-3803-5703
mit.licenseOPEN_ACCESS_POLICYen_US


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