For the problem max{Z(S): S is an independent set in the matroid X}, it is well-known that the greedy algorithm finds an optimal solution when Z is an additive set function (RadoEdmonds theorem).… (More)

A 0; 1 matrix is balanced if it does not contain a square submatrix of odd order with two ones per row and per column. We show that a balanced 0,1 matrix is either totally unimodular or its bipartite… (More)

Recently, it has been shown that minimal inequalities for a continuous relaxation of mixed integer linear programs are associated with maximal lattice-free convex sets. In this paper we show how to… (More)

We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some rational polyhedron of R. This result extends a theorem of Lovász characterizing maximal… (More)

In Mathematical Programming 2003, Gomory and Johnson conjecture that the facets of the infinite group problem are always generated by piecewise linear functions. In this paper we give an example… (More)

We consider a model that arises in integer programming, and show that all irredundant inequalities are obtained from maximal lattice-free convex sets in an affine subspace. We also show that these… (More)

This survey is concerned with the size of perfect formulations for combinatorial optimization problems. By “perfect formulation”, we mean a system of linear inequalities that describes the convex… (More)