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One of the classic results in scheduling theory is the 2-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines; i.e., job j requires time p(ij) if processed on machine i. More t ...
We revisit simultaneous diophantine approximation, a classical problem from the geometry of numbers which has many applications in algorithms and complexity. The input of the decision version of this problem consists of a rational vector \alpha, an error b ...
One of the classic results in scheduling theory is the 2-approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines, i.e., job j requires time p ij if processed on machine i. More th ...
We consider the problem of testing whether the maximum integrality gap of a family of integer programs in standard form is bounded by a given constant. This can be viewed as a generalization of the integer rounding property, which can be tested in polynomi ...
We consider an extension of integer linear arithmetic with a star operator that takes closure under vector addition of the set of solutions of linear arithmetic subformula. We show that the satisfiability problem for this language is in NP (and therefore N ...
We consider an extension of integer linear arithmetic with a “star” operator takes closure under vector addition of the solution set of a linear arithmetic subformula. We show that the satisfiability problem for this extended language remains in NP (and th ...
We consider the following problem: Given a rational matrix A∈Qm×n and a rational polyhedron Q⊆Rm+p, decide if for all vectors b∈Rm, for which there exists an integral z∈Zp suc ...
Summary form only given. Integer programming is the problem of maximizing a linear function over the integer vectors which satisfy a given set of inequalities. A wide range of combinatorial optimization problems can be modeled as integer programming proble ...
We analyze a short-term revenue optimization problem that involves the optimal targeting of customers for a promotion in which a finite number of perishable items are sold on a last-minute offer. The goal is to select the subset of customers to whom the of ...
We consider mixed-integer sets described by system of linear inequalities in which the constraint matrix A is totally unimodular; the right-hand side is arbitrary vector; and a subset of the variables is required to be integer. We show that the problem of ...
