Improved approximations for the steiner tree problem

Piotr Berman, Vishwanathan Ramaiyer

    Research output: Contribution to journalArticlepeer-review

    131 Scopus citations


    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 the rectilinear metric on the plane. Our method offers a trade-off between the running time and the ratio: on one hand it always allows improvement of the ratio, on the other hand it allows previously known ratios to be obtained with greater efficiency. We use properties of optimal rectilinear Steiner trees to obtain significantly better ratio and running time in the rectilinear metric.

    Original languageEnglish (US)
    Pages (from-to)381-408
    Number of pages28
    JournalJournal of Algorithms
    Issue number3
    StatePublished - Nov 1994

    All Science Journal Classification (ASJC) codes

    • Computational Mathematics
    • Control and Optimization
    • Computational Theory and Mathematics


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