The Stretch Factor of the Delaunay Triangulation Is Less than 1.998
نویسندگان
چکیده
منابع مشابه
The Stretch Factor of the Delaunay Triangulation Is Less than 1.998
Let S be a finite set of points in the Euclidean plane. Let D be a Delaunay triangulation of S. The stretch factor (also known as dilation or spanning ratio) of D is the maximum ratio, among all points p and q in S, of the shortest path distance from p to q in D over the Euclidean distance ||pq||. Proving a tight bound on the stretch factor of the Delaunay triangulation has been a long standing...
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The problem of computing the exact stretch factor (i.e., the tight bound on the worst case stretch factor) of a Delaunay triangulation has been open for more than three decades. 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 comp...
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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 dilation 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 po...
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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 dilation 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 po...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2013
ISSN: 0097-5397,1095-7111
DOI: 10.1137/110832458