A Note on Submodular Functions on Distributive Lattices
نویسندگان
چکیده
A NOTE ON SUBMODULAR FUNCTIONS ON DISTRIBUTIVE LATTICES Satoru Fujishige University of Tsukuba Nobuaki Tomizawa Niigata University (Received July 15, 1982; Rllvised June 14, 1983) Let D be a distributive lattice formed by subsets of a finite set E with 1/>, E E D and let R be the set of reals. Also let f be a submodular function from D into R with f(l/» = O. We determine the set of extreme points of the base polyhedron 8(t) = I x I x ERE, x(X) ~ f(X) (X E D), x(E) = feE) I and give upper and lower bounds of f which can be obtained in polynomial time in IEI under mild assumptiOl\s.
منابع مشابه
Weakly submodular rank functions, supermatroids, and the flat lattice of a distributive supermatroid
Distributive supermatroids generalize matroids to partially ordered sets. Completing earlier work of Barnabei, Nicoletti and Pezzoli we characterize the lattice of flats of a distributive supermatroid. For the prominent special case of a polymatroid the description of the flat lattice is particularly simple. Large portions of the proofs reduce to properties of weakly submodular rank functions. ...
متن کاملDistributive lattices with strong endomorphism kernel property as direct sums
Unbounded distributive lattices which have strong endomorphism kernel property (SEKP) introduced by Blyth and Silva in [3] were fully characterized in [11] using Priestley duality (see Theorem 2.8}). We shall determine the structure of special elements (which are introduced after Theorem 2.8 under the name strong elements) and show that these lattices can be considered as a direct product of ...
متن کاملCoproducts of bounded distributive lattices: cancellation
Let L ∗ M denote the coproduct of the bounded distributive lattices L and M . At the 1981 Banff Conference on Ordered Sets, the following question was posed: What is the largest class L of finite distributive lattices such that, for every non-trivial Boolean lattice B and every L ∈ L, B ∗ L = B ∗ L′ implies L = L′? In this note, the problem is solved.
متن کاملCoproducts of Bounded Distributive Lattices
Let LM denote the coproduct of the bounded distributive lattices L and M. At the 1981 Bann Conference on Ordered Sets, the following question was posed: What is the largest class L of nite distributive lattices such that, for every non-trivial Boolean lattice B and every L 2 L, B L = B L 0 implies L = L 0 ? In this note, the problem is solved.
متن کاملMatroids on convex geometries (cg-matroids)
We consider matroidal structures on convex geometries, which we call cg-matroids. The concept of a cg-matroid is closely related to but different from that of a supermatroid introduced by Dunstan, Ingleton, and Welsh in 1972. Distributive supermatroids or poset matroids are supermatroids defined on distributive lattices or sets of order ideals of posets. The class of cg-matroids includes distri...
متن کامل