A Finite Algorithm for the Realizabilty of a Delaunay Triangulation

Akanksha Agrawal, Saket Saurabh, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The Delaunay graph of a point set P ⊆ R2 is the plane graph with the vertex-set P and the edge-set that contains {p, p} if there exists a disc whose intersection with P is exactly {p, p}. Accordingly, a triangulated graph G is Delaunay realizable if there exists a triangulation of the Delaunay graph of some P ⊆ R2, called a Delaunay triangulation of P, that is isomorphic to G. The objective of Delaunay Realization is to compute a point set P ⊆ R2 that realizes a given graph G (if such a P exists). Known algorithms do not solve Delaunay Realization as they are non-constructive. Obtaining a constructive algorithm for Delaunay Realization was mentioned as an open problem by Hiroshima et al. [19]. We design an nO(n)-time constructive algorithm for Delaunay Realization. In fact, our algorithm outputs sets of points with integer coordinates.

Original languageEnglish
Title of host publication17th International Symposium on Parameterized and Exact Computation, IPEC 2022
EditorsHolger Dell, Jesper Nederlof
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages1:1-1:16
Number of pages16
Volume249
ISBN (Electronic)9783959772600
DOIs
StatePublished - 14 Dec 2022
Event17th International Symposium on Parameterized and Exact Computation, IPEC 2022 - Potsdam, Germany
Duration: 7 Sep 20229 Sep 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume249
ISSN (Print)1868-8969

Conference

Conference17th International Symposium on Parameterized and Exact Computation, IPEC 2022
Country/TerritoryGermany
CityPotsdam
Period7/09/229/09/22

Keywords

  • Delaunay Realization
  • Delaunay Triangulation
  • Finite Algorithm
  • Integer Coordinate Realization

ASJC Scopus subject areas

  • Software

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