On greedy and submodular matrices

Authors:
Ulrich Faigle;Walter Kern;Britta Peis
Affiliations:
Math. Institut, Universität zu Köln, Köln;Universiteit Twente, Enschede;Technische Universität Berlin, Berlin
Venue:
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
Year:
2011

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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.