The computational complexity of the k-minimum spanning tree problem in graded matrices

T. Dudás, B. Klinz, G.J. Woeginger

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    3 Citaten (Scopus)

    Samenvatting

    Given an undirected graph G = (V, E) where each edge e = (i, j) has a length dij = 0, the ¿-minimum spanning tree problem, ¿-MST for short, is to find a tree T in G which spans at least ¿ vertices and has minimum length l(T) = ¿(i,j)e Tdij. We investigate the computational complexity of the ¿-minimum spanning tree problem in complete graphs when the distance matrix D = (dij) is graded, i.e., has increasing, respectively, decreasing rows, or increasing, respectively, decreasing columns, or both. We exactly characterize polynomially solvable and NP-complete variants, and thus, establish a sharp borderline between easy and difficult cases of the ¿-MST problem on graded matrices. As a somewhat surprising result, we prove that the problem is polynomially solvable on graded matrices with decreasing rows, but NP-complete on graded matrices with increasing rows.
    Originele taal-2Engels
    Pagina's (van-tot)61-67
    Aantal pagina's7
    TijdschriftComputers and Mathematics with Applications
    Volume36
    Nummer van het tijdschrift5
    DOI's
    StatusGepubliceerd - 1998

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