# 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 language English Enschede University of Twente, Faculty of Mathematical Sciences 12 Published - 1993

### Publication series

Name Memorandum University of Twente, Department of Computer Science 1172 0924-3755

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• ### A characterization of non-negative greedy matrices

Faigle, U., Hoffman, A. J. & Kern, W., 1996, 9, 1, p. 1-6 6 p.