Theory of linear and integer programming
Theory of linear and integer programming
Mathematical Programming: Series A and B
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A new class of polyhedra, named greedy-type polyhedra, is introduced. This class contains polyhedra associated with submodular set functions. Greedy-type polyhedra are associated with submodular functions defined on 012-vectors and have 012-vectors as normal vectors of their facets. The face structure of greedy-type polyhedra is described with maximal chains of a certain partial order defined on 012-vectors. Integrality of polyhedra associated with integral greedy-type functions is shown through total dual integrality of the systems of inequalities defining polyhedra. Then a dual algorithm maximizing linear functions over these polyhedra is proposed. It is shown that feasible outputs of certain bipartite networks with gain make greedy-type polyhedra. A separation theorem for greedy-type functions is also proved.