Abstract
In this paper we determine the stretch factor of L 1-Delaunay and L ∞ -Delaunay triangulations, and we show that it is equal to \(\sqrt{4+2\sqrt{2}} \approx 2.61\). Between any two points x,y of such triangulations, we construct a path whose length is no more than \(\sqrt{4+2\sqrt{2}}\) times the Euclidean distance between x and y, and this bound is the best possible. This definitively improves the 25-year old bound of \(\sqrt{10}\) by Chew (SoCG ’86). This is the first time the stretch factor of the L p -Delaunay triangulations, for any real p ≥ 1, is determined exactly.
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Bonichon, N., Gavoille, C., Hanusse, N., Perković, L. (2012). The Stretch Factor of L 1- and L ∞ -Delaunay Triangulations. In: Epstein, L., Ferragina, P. (eds) Algorithms – ESA 2012. ESA 2012. Lecture Notes in Computer Science, vol 7501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33090-2_19
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DOI: https://doi.org/10.1007/978-3-642-33090-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33089-6
Online ISBN: 978-3-642-33090-2
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