On the number of minimal 1-Steiner trees

B. Aronov, M. Bern, D. Eppstein

    Research output: Contribution to journalArticle

    Abstract

    We count the number of nonisomorphic geometric minimum spanning trees formed by adding a single point to an n-point set in d-dimensional space, by relating it to a family of convex decompositions of space. The O(n d log2 d 2-d n) bound that we obtain significantly improves previously known bounds and is tight to within a polylogarithmic factor.

    Original languageEnglish (US)
    Pages (from-to)29-34
    Number of pages6
    JournalDiscrete and Computational Geometry
    Volume12
    Issue number1
    DOIs
    StatePublished - Dec 1994

    Fingerprint

    Steiner Tree
    Convex Decomposition
    Decomposition
    Minimum Spanning Tree
    Point Sets
    Count
    Family

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Discrete Mathematics and Combinatorics
    • Computational Theory and Mathematics

    Cite this

    On the number of minimal 1-Steiner trees. / Aronov, B.; Bern, M.; Eppstein, D.

    In: Discrete and Computational Geometry, Vol. 12, No. 1, 12.1994, p. 29-34.

    Research output: Contribution to journalArticle

    Aronov, B. ; Bern, M. ; Eppstein, D. / On the number of minimal 1-Steiner trees. In: Discrete and Computational Geometry. 1994 ; Vol. 12, No. 1. pp. 29-34.
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