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There are planar graphs almost as good as the complete graphs and almost as cheap as minimum spanning trees

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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)[2π/3 cos(π/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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Authors and Affiliations

  1. Department of Computer Science and Numerical Analysis, Lund University, Box 118, 221 00, Lund, Sweden

    Christos Levcopoulos & Andrzej Lingas

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  1. Christos Levcopoulos
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  2. Andrzej Lingas
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Communicated by Greg. N. Frederickson.

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Levcopoulos, C., Lingas, A. There are planar graphs almost as good as the complete graphs and almost as cheap as minimum spanning trees. Algorithmica 8, 251–256 (1992). https://doi.org/10.1007/BF01758846

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  • DOI: https://doi.org/10.1007/BF01758846

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