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On steiner ratio conjectures

  • Section VI Steiner Tree Networks
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Abstract

LetM be a metric space andP a finite set of points inM. The Steiner ratio inM is defined to beρ(M)=inf{L s(P)/L m(P) |P ⊂M}, whereL s(P) andL m(P) are the lengths of the Steiner minimal tree and the minimal spanning tree onP, respectively. In this paper, we study various conjectures onρ(M). In particular, we show that forn-dimensional Euclidean spaceℝ n ,ρ(ℝ n )>0.615.

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Authors and Affiliations

  1. Department of Computer Science, Princeton University, USA

    Ding-Zhu Du

  2. Academia Sinica, Institute of Applied Mathematics, Beijing, People's Republic of China

    Ding-Zhu Du

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  1. Ding-Zhu Du
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Supported in part by the National Science Foundation of China.

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Du, DZ. On steiner ratio conjectures. Ann Oper Res 33, 437–449 (1991). https://doi.org/10.1007/BF02071981

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  • DOI: https://doi.org/10.1007/BF02071981

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