A characterization of non-negative greedy matrices

Ulrich Faigle, Walter Kern

    Research output: Book/ReportReportProfessional

    Abstract

    Given an ordering of the variables according to nonincreasing coefficients of the objective function $c^T x$, the nonnegative matrix A is said to be greedy if, under arbitrary nonnegative constraint vectors b and h, the greedy algorithm maximizes $c^T x$ subject to $Ax \leq b,0 \leq x \leq h$. Extending a result of Hoffman, Kolen, and Sakarovitch for $(0,1)$-matrices, we characterize greedy matrices in terms of forbidden submatrices, which yields polynomial recognition algorithms for various classes of greedy matrices. The general recognition problem for the existence of forbidden submatrices is shown to be NP-complete.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Faculty of Mathematical Sciences
    Number of pages12
    Publication statusPublished - 1993

    Publication series

    NameMemorandum
    PublisherUniversity of Twente, Department of Computer Science
    No.1172
    ISSN (Print)0924-3755

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