---
_id: '1173'
abstract:
- lang: eng
  text: We introduce the Voronoi functional of a triangulation of a finite set of
    points in the Euclidean plane and prove that among all geometric triangulations
    of the point set, the Delaunay triangulation maximizes the functional. This result
    neither extends to topological triangulations in the plane nor to geometric triangulations
    in three and higher dimensions.
acknowledgement: This research is partially supported by the Russian Government under
  the Mega Project 11.G34.31.0053, by the Toposys project FP7-ICT-318493-STREP, by
  ESF under the ACAT Research Network Programme, by RFBR grant 11-01-00735, and by
  NSF grants DMS-1101688, DMS-1400876.
article_processing_charge: No
author:
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Alexey
  full_name: Glazyrin, Alexey
  last_name: Glazyrin
- first_name: Oleg
  full_name: Musin, Oleg
  last_name: Musin
- first_name: Anton
  full_name: Nikitenko, Anton
  id: 3E4FF1BA-F248-11E8-B48F-1D18A9856A87
  last_name: Nikitenko
  orcid: 0000-0002-0659-3201
citation:
  ama: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. The Voronoi functional is
    maximized by the Delaunay triangulation in the plane. <i>Combinatorica</i>. 2017;37(5):887-910.
    doi:<a href="https://doi.org/10.1007/s00493-016-3308-y">10.1007/s00493-016-3308-y</a>
  apa: Edelsbrunner, H., Glazyrin, A., Musin, O., &#38; Nikitenko, A. (2017). The
    Voronoi functional is maximized by the Delaunay triangulation in the plane. <i>Combinatorica</i>.
    Springer. <a href="https://doi.org/10.1007/s00493-016-3308-y">https://doi.org/10.1007/s00493-016-3308-y</a>
  chicago: Edelsbrunner, Herbert, Alexey Glazyrin, Oleg Musin, and Anton Nikitenko.
    “The Voronoi Functional Is Maximized by the Delaunay Triangulation in the Plane.”
    <i>Combinatorica</i>. Springer, 2017. <a href="https://doi.org/10.1007/s00493-016-3308-y">https://doi.org/10.1007/s00493-016-3308-y</a>.
  ieee: H. Edelsbrunner, A. Glazyrin, O. Musin, and A. Nikitenko, “The Voronoi functional
    is maximized by the Delaunay triangulation in the plane,” <i>Combinatorica</i>,
    vol. 37, no. 5. Springer, pp. 887–910, 2017.
  ista: Edelsbrunner H, Glazyrin A, Musin O, Nikitenko A. 2017. The Voronoi functional
    is maximized by the Delaunay triangulation in the plane. Combinatorica. 37(5),
    887–910.
  mla: Edelsbrunner, Herbert, et al. “The Voronoi Functional Is Maximized by the Delaunay
    Triangulation in the Plane.” <i>Combinatorica</i>, vol. 37, no. 5, Springer, 2017,
    pp. 887–910, doi:<a href="https://doi.org/10.1007/s00493-016-3308-y">10.1007/s00493-016-3308-y</a>.
  short: H. Edelsbrunner, A. Glazyrin, O. Musin, A. Nikitenko, Combinatorica 37 (2017)
    887–910.
date_created: 2018-12-11T11:50:32Z
date_published: 2017-10-01T00:00:00Z
date_updated: 2023-09-20T11:23:53Z
day: '01'
department:
- _id: HeEd
doi: 10.1007/s00493-016-3308-y
ec_funded: 1
external_id:
  isi:
  - '000418056000005'
intvolume: '        37'
isi: 1
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1411.6337
month: '10'
oa: 1
oa_version: Submitted Version
page: 887 - 910
project:
- _id: 255D761E-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '318493'
  name: Topological Complex Systems
publication: Combinatorica
publication_identifier:
  issn:
  - '02099683'
publication_status: published
publisher: Springer
publist_id: '6182'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Voronoi functional is maximized by the Delaunay triangulation in the plane
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 37
year: '2017'
...