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A proof of the Gilbert-Pollak conjecture on the Steiner ratio

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Abstract

LetP be a set ofn points on the euclidean plane. LetL s(P) andL m (P) denote the lengths of the Steiner minimum tree and the minimum spanning tree onP, respectively. In 1968, Gilbert and Pollak conjectured that for anyP,L s (P)≥(√3/2)L m (P). We provide a proof for their conjecture in this paper.

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Authors and Affiliations

  1. Department of Computer Science, Princeton University, USA

    D. -Z. Du

  2. DIMACS (Center for Discrete Mathematics and Theoretical Computer Science), a National Science Foundation Science and Technology Center, USA

    D. -Z. Du

  3. Institute of Applied Mathematics, Academia Sinica, Beijing, China

    D. -Z. Du

  4. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA

    F. K. Hwang

Authors
  1. D. -Z. Du
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  2. F. K. Hwang
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Additional information

Communicated by F. K. Hwang.

supported by NSF under grant STC88-09648.

supported in part by the National Natural Science Foundation of China.

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Du, D.Z., Hwang, F.K. A proof of the Gilbert-Pollak conjecture on the Steiner ratio. Algorithmica 7, 121–135 (1992). https://doi.org/10.1007/BF01758755

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  • DOI: https://doi.org/10.1007/BF01758755

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