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- W1993585122 abstract "Consider the Delaunay triangulation T of a set P of points in the plane as a Euclidean graph, in which the weight of every edge is its length. It has long been conjectured that the stretch factor in T of any pair p,p′∈P, which is the ratio of the length of the shortest path from p to p′ in T over the Euclidean distance ‖pp′‖, can be at most π/2≈1.5708. In this paper, we show how to construct point sets in convex position with stretch factor >1.5810 and in general position with stretch factor >1.5846. Furthermore, we show that a sufficiently large set of points drawn independently from any distribution will in the limit approach the worst-case stretch factor for that distribution." @default.
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- W1993585122 date "2011-02-01" @default.
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- W1993585122 title "Almost all Delaunay triangulations have stretch factor greater than <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:mi>π</mml:mi><mml:mo stretchy=false>/</mml:mo><mml:mn>2</mml:mn></mml:math>" @default.
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- W1993585122 doi "https://doi.org/10.1016/j.comgeo.2010.09.009" @default.
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