TY - JOUR
T1 - A characterization of non-negative greedy matrices
AU - Faigle, Ulrich
AU - Hoffman, Alan J.
AU - Kern, Walter
PY - 1996
Y1 - 1996
N2 - 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.
AB - 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.
KW - Greedy algorithm
KW - Linear program
U2 - 10.1137/0409001
DO - 10.1137/0409001
M3 - Article
SN - 0895-4801
VL - 9
SP - 1
EP - 6
JO - SIAM journal on discrete mathematics
JF - SIAM journal on discrete mathematics
IS - 1
ER -