Note on pseudolattices, lattices and submodular linear programs

13 years 4 months ago

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A pseudolattice L is a poset with lattice-type binary operations. Assuming that the pseudolattice permits a modular representation as a family of subsets of a set U with certain compatibility properties, we show that L actually is a distributive lattice with the same supremum operation. Given a submodular function r : L R, we prove that the corresponding unrestricted linear program relative to the representing set family can be solved by a greedy algorithm. This complements the Monge algorithm of Dietrich and Hoffman for the associated dual linear program. We furthermore show that our Monge and greedy algorithm is generally optimal for nonnegative submodular linear programs and their duals (relative to L).

Ulrich Faigle, Britta Peis

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