2015
DOI: 10.1016/j.comgeo.2014.10.005
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Tight stretch factors for L1- and L-Delaunay triangulations

Abstract: In this paper we determine the exact stretch factor of L ∞ -Delaunay triangulations of points in the plane. We do this not only when the distance between the points is defined by the usual L 2 -metric but also when it is defined by the L p -metric, for any p ∈ [1, ∞]. We then apply this result to compute the exact stretch factor of L 1 -Delaunay triangulations when the distance between the points is defined by the L 1 -, L ∞ -, or L 2 -metric. In the important case of the L 2 -metric, we obtain that the stretc… Show more

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Cited by 8 publications
(9 citation statements)
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References 13 publications
(16 reference statements)
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“…Our approach in proving Theorem 5 mimics the approach used in [2] to establish a stretch factor of 4 + 2 √ 2 for Del ∞ . Before describing this approach, we need to introduce some definitions.…”
Section: Definitionsmentioning
confidence: 99%
See 1 more Smart Citation
“…Our approach in proving Theorem 5 mimics the approach used in [2] to establish a stretch factor of 4 + 2 √ 2 for Del ∞ . Before describing this approach, we need to introduce some definitions.…”
Section: Definitionsmentioning
confidence: 99%
“…Before describing this approach, we need to introduce some definitions. To make it easy for the interested reader, most of the terminology in this section is similar to the one used in [2]. We assume without loss of generality that a has coordinates (0, 0).…”
Section: Definitionsmentioning
confidence: 99%
“…An analogous construction works with circles (or squares) replaced by any convex, centrally symmetric plane shape C, provided no straight segment between singularities is parallel to a segment of ∂C. See [12] for related ideas in dimension at least 2, as well as [2] and references therein. Proposition 2.1.…”
Section: The Canonical Veering Triangulationmentioning
confidence: 99%
“…Remarks 5.1 and 5.2 above, and the bijectivity of the dictionary, imply that the edges of the Cannon-Thurston tessellation are obtained from the Agol triangulation by drawing an edge between the tip of each triangle and the tip of the next triangle across its base rung. This gives the recipe in the first direction of Theorem 1.3 (2).…”
Section: The Recipe Book or Theorem 13(2)mentioning
confidence: 99%
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