eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-08
34:1
34:16
10.4230/LIPIcs.SoCG.2020.34
article
The Stretch Factor of Hexagon-Delaunay Triangulations
Dennis, Michael
1
Perković, Ljubomir
2
Türkoğlu, Duru
2
Computer Science Division, University of California at Berkeley, Berkeley, CA, USA
School of Computing, DePaul University, Chicago, IL, USA
The problem of computing the exact stretch factor (i.e., the tight bound on the worst case stretch factor) of a Delaunay triangulation is one of the longstanding open problems in computational geometry. Over the years, a series of upper and lower bounds on the exact stretch factor have been obtained but the gap between them is still large. An alternative approach to solving the problem is to develop techniques for computing the exact stretch factor of "easier" types of Delaunay triangulations, in particular those defined using regular-polygons instead of a circle. Tight bounds exist for Delaunay triangulations defined using an equilateral triangle and a square. In this paper, we determine the exact stretch factor of Delaunay triangulations defined using a regular hexagon: It is 2. We think that the main contribution of this paper are the two techniques we have developed to compute tight upper bounds for the stretch factor of Hexagon-Delaunay triangulations.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol164-socg2020/LIPIcs.SoCG.2020.34/LIPIcs.SoCG.2020.34.pdf
Delaunay triangulation
geometric spanner
plane spanner
stretch factor
spanning ratio