Theory of linear and integer programming
Theory of linear and integer programming
On greedy and submodular matrices
TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
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We reexamine the class of (0,±1) matrices called submodular, which we introduced in (Ann. Discrete Math. 15 (1982) 189). Our key idea in this paper is to define, for each submodular matrix M, a corresponding digraph G whose nodes are the columns of M. Our principal results are as follows: (a) a graph-theoretic interpretation of the polyhedron P(M) = {x: x ≥ 0, Mx ≥ - 1}, and (b) for a given G, the description of a submodular matrix contained in all submodular matrices representing G.