In this paper we explore the geometry of the integer points in a cone rooted at a rational point. This basic geometric object allows us to establish some links between lattice point free bodies andâ€¦ (More)

In this survey we address three of the principal algebraic approaches to integer programming. After introducing lattices and basis reduction, we 0rst survey their use in integer programming,â€¦ (More)

Cellular decisions are determined by complex molecular interaction networks. Large-scale signaling networks are currently being reconstructed, but the kinetic parameters and quantitative data thatâ€¦ (More)

Given a set N of items and a capacity b 2 IN, and let N j be the set of items with weight j, 1 j b. The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy the inequality b X j=1â€¦ (More)

This survey presents cutting planes that are useful or potentially useful in solving mixed integer programs. Valid inequalities for i) general integer programs, ii) problems with local structure suchâ€¦ (More)

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reachedâ€¦ (More)

In the context of a variation of the standard UFL (Uncapacitated Facility Location) problem, but with an objective function that is a separable convex quadratic function of the transportation costs,â€¦ (More)