A NOTE ON SUBMODULAR FUNCTIONS ON DISTRIBUTIVE LATTICES

Abstract

Let D be a distributive lattice formed by subsets of a finite set E with φ, E ∈ D and let R be the set of' reals. Also let f be a submodular function from D into R with f(φ) = 0. We determine the set of extreme points of the base polyhedron [numerical formula] and give upper and lower bounds of f which can be obtained in polynomial time in |E| under mild assumptions.