Improved approximations for the steiner tree problem

Piotr Berman, Viswanathan Ramaiyer

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    39 Scopus citations

    Abstract

    For a set S contained in a metric space, a Steiner tree of S is a tree that connects the points in S. Finding a minimum cost Steiner tree is an NP-hard problem in euclidean and rectilinear metrics as well as in graphs. We give an approximation algorithm and show that the worst-case ratio of the cost of our solutions to the optimal cost is better than previously known ratios in graphs, and in rectilinear metric on the plane. Our method offers a tradeoff between the running time and the ratio; on one hand it always allows to improve the ratio, on the other it allows to obtain previously known ratios with much greater efficiency. We use properties of optimal rectilinear Steiner trees to obtain significantly better ratio and running time in rectilinear metric.

    Original languageEnglish (US)
    Title of host publicationProceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
    PublisherAssociation for Computing Machinery
    Pages325-334
    Number of pages10
    ISBN (Electronic)089791466X
    StatePublished - Sep 1 1992
    Event3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 - Orlando, United States
    Duration: Jan 27 1992Jan 29 1992

    Publication series

    NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
    VolumePart F129721

    Other

    Other3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
    CountryUnited States
    CityOrlando
    Period1/27/921/29/92

    All Science Journal Classification (ASJC) codes

    • Software
    • Mathematics(all)

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  • Cite this

    Berman, P., & Ramaiyer, V. (1992). Improved approximations for the steiner tree problem. In Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 (pp. 325-334). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. Part F129721). Association for Computing Machinery.