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The steiner ratio for five points

  • Section VI Steiner Tree Networks
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Abstract

It was conjectured by Gilbert and Pollak [5] that for any finite set of points in the Euclidean plane, the ratio of the length of a Steiner minimal tree to the length of a minimal spanning tree is at least √3/2. The present paper proves the conjecture for five points, using a formula for the length of full Steiner trees.

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References

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Authors and Affiliations

  1. The School of Mathematical Sciences, The Flinders University of South Australia, 5042, Bedford Park, S.A., Australia

    R. S. Booth

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  1. R. S. Booth
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Booth, R.S. The steiner ratio for five points. Ann Oper Res 33, 419–436 (1991). https://doi.org/10.1007/BF02071980

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  • DOI: https://doi.org/10.1007/BF02071980

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