Delaunay graphs are almost as good as complete graphs (Q584279)
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scientific article; zbMATH DE number 4134086
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Delaunay graphs are almost as good as complete graphs |
scientific article; zbMATH DE number 4134086 |
Statements
Delaunay graphs are almost as good as complete graphs (English)
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1990
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Let S be a set of N points in the plane and let DT(S) be the graph of the Delaunay triangulation of S. For all points a and b of S, let d(a,b) be the Euclidean distance from a to b and let DT(a,b) be the length of the shortest path in DT(S) from a to b. We show that there is a constant c \((\leq ((1+\sqrt{5})/2)\pi \approx 5.08)\) independent of S and N such that \(\frac{DT(a,b)}{d(a,b)}<c.\)
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Delaunay triangulation
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Euclidean distance
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shortest path
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