There are planar graphs almost as good as the complete graphs and almost as cheap as minimum spanning trees |
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Authors: | Christos Levcopoulos and Andrzej Lingas |
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Affiliation: | (1) Department of Computer Science and Numerical Analysis, Lund University, Box 118, 221 00 Lund, Sweden |
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Abstract: | Let S be a set ofn points in the plane. For an arbitrary positive rationalr, we construct a planar straight-line graph onS that approximates the complete Euclidean graph onS within the factor (1 + 1/r)2/3 cos(/6)], and it has length bounded by 2r + 1 times the length of a minimum Euclidean spanning tree onS. Given the Deiaunay triangulation ofS, the graph can be constructed in linear time. |
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Keywords: | Planar graph Minimum spanning tree Complete graph Delaunay triangulation Time complexity |
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