On greedy and submodular matrices

Abstract

We characterize non-negative greedy matrices, i.e., (0,1)-matrices A such that the problem max {cT x|Ax ≤ b, x ≥0} can be solved greedily. We identify so-called submodular matrices as a special subclass of greedy matrices. Finally, we extend the notion of greediness to {-1,0,1}-matrices. We present numerous applications of these concepts. © 2011 Springer-Verlag.