Approximating the minimum-degree steiner tree to within one of optimal

Martin Fürer, Balaji Raghavachari

    Research output: Contribution to journalArticlepeer-review

    151 Scopus citations


    The problem of constructing a spanning tree for a graph G = (V, E) with n vertices whose maximal degree is the smallest among all spanning trees of G is considered. This problem is easily shown to be NP-hard. In the Steiner version of this problem, along with the input graph, a set of distinguished vertices D ⊆ V is given. A minimum-degree Steiner tree is a tree of minimum degree which spans at least the set D. Iterative polynomial time approximation algorithms for the problems are given. The algorithms compute trees whose maximal degree is at most Δ* + 1, where Δ* is the degree of some optimal tree for the respective problems. Unless P = NP, this is the best bound achievable in polynomial time.

    Original languageEnglish (US)
    Pages (from-to)409-423
    Number of pages15
    JournalJournal of Algorithms
    Issue number3
    StatePublished - Nov 1994

    All Science Journal Classification (ASJC) codes

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


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