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Mosc. Math. J., 2014, Volume 14, Number 3, Pages 491–504 (Mi mmj530)  

This article is cited in 2 scientific papers (total in 2 papers)

Functionals on triangulations of Delaunay sets

Nikolay P. Dolbilina, Herbert Edelsbrunnerb, Alexey Glazyrinc, Oleg R. Musincd

a Department of Geometry and Topology, Steklov Mathematical Institute, 8, Gubkina str., 119991, Moscow, Russia
b Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria
c Department of Mathematics, University of Texas at Brownsville, One West University Boulevard, Brownsville, Texas 78520, USA
d The Institute for Information Transmission Problems (Kharkevich Institute), Russian Academy of Sciences, Bolshoy Karetny per. 19, Moscow, 127994, Russia

Abstract: We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets.

Key words and phrases: Delaunay sets, triangulations, Delaunay triangulations, uniformly bounded triangulations, functionals, densities.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 11.G34.31.0053
Russian Foundation for Basic Research 11-01-00735
National Science Foundation DMS 1101688
European Science Foundation
This research is supported by the Delone Laboratory of Discrete and Computational Geometry, Yaroslavl State University, Russia, under the Russian Government Mega Project 11.G34.31.0053, RFBR grant 11-01-00735, DMS 1101688, and the European Science Foundation (ESF) under the Research Network Programme.


Full text: http://www.mathjournals.org/.../2014-014-003-003.html
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Document Type: Article
MSC: 52C20, 52C22
Received: January 13, 2012
Language: English

Citation: Nikolay P. Dolbilin, Herbert Edelsbrunner, Alexey Glazyrin, Oleg R. Musin, “Functionals on triangulations of Delaunay sets”, Mosc. Math. J., 14:3 (2014), 491–504

Citation in format AMSBIB
\Bibitem{DolEdeGla14}
\by Nikolay~P.~Dolbilin, Herbert~Edelsbrunner, Alexey~Glazyrin, Oleg~R.~Musin
\paper Functionals on triangulations of Delaunay sets
\jour Mosc. Math.~J.
\yr 2014
\vol 14
\issue 3
\pages 491--504
\mathnet{http://mi.mathnet.ru/mmj530}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3241757}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000342789400003}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Klyachin, “Ekstremalnye svoistva triangulyatsii, osnovannoi na uslovii pustogo vypuklogo mnozhestva”, Sib. elektron. matem. izv., 12 (2015), 991–997  mathnet  crossref
    2. H. Edelsbrunner, A. Glazyrin, O. R. Musin, A. Nikitenko, “The Voronoi functional is maximized by the Delaunay triangulation in the plane”, Combinatorica, 37:5 (2017), 887–910  crossref  mathscinet  zmath  isi  scopus
  • Moscow Mathematical Journal
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