We introduce new classes of valid inequalities, called wheel inequalities, for the stable set polytope P G of a graph G. Each \wheel connguration" gives rise to two such inequalities. The simplest wheel connguration is an \odd" subdivision W of a wheel, and for these we give necessary and suucient conditions for the wheel inequality to be facet-inducing for P W. Generalizations arise by allowin...

Bit-vector arithmetic operations rely on modular arithmetic semantics, which often complicates algebraic manipulations. One such example are inequalities. Satisfiability of a system of modular inequalities is NP-complete [1]. In this memo we investigate a simple type of inequalities: only one variable is permitted and there are no multiplications. Satisfiability is solved in polynomial time by ...

An explicit description of the convex hull of solutions to the uncapacitated lot-sizing problem with backlogging, in its natural space of production, setup, inventory and backlogging variables, has been an open question for many years. In this paper, we identify valid inequalities that subsume all previously known valid inequalities for this problem. We show that these inequalities are enough t...

Newton’s inequalities cn ≥ cn−1cn+1 are shown to hold for the normalized coefficients cn of the characteristic polynomial of any Mor inverse M-matrix. They are derived by establishing first an auxiliary set of inequalities also valid for both of these classes. They are also used to derive some new necessary conditions on the eigenvalues of nonnegative matrices.

Brascamp-Lieb inequalities [5] is an important mathematical tool in analysis, geometry and information theory. There are various ways to prove Brascamp-Lieb inequality such as heat flow method [4], Brownian motion [11] and subadditivity of the entropy [6]. While Brascamp-Lieb inequality is originally stated in Euclidean Space, [8] discussed Brascamp-Lieb inequality for discrete Abelian group an...

We consider the network design problem which consists in determining at minimum cost a 2-edge connected network such that the shortest cycle (a “ring”) to which each edge belongs, does not exceed a given length K. We identify a class of valid inequalities, called cycle inequalities, valid for the problem and show that this inequalities together with the so-called cut inequalities yield an integ...

In this paper, we study a multi-echelon uncapacitated lot-sizing problem in series (mULS), where the output of the intermediate echelons has its own external demand, and is also an input to the next echelon. We propose a polynomial-time dynamic programming algorithm, which gives a tight, compact extended formulation for the two echelon case (2-ULS). Next, we present a family of valid inequaliti...

Let 0 < j < m ≤ n be integers. Denote by ‖ · ‖ the norm ‖f‖2 = ∫∞ −∞ f 2(x) exp(−x2)dx. For various positive values of A and B we establish Kolmogoroff type inequalities ‖f ‖ ≤ A‖f (m)‖2 +B‖f‖2 Aθk +Bμk , with certain constants θk e μk, which hold for every f ∈ πn (πn denotes the space of real algebraic polynomials of degree not exceeding n). For the particular case j = 1 and m = 2, we provide ...

This paper studies the complexity of type inference in-calculus with subtyping. Type inference is equivalent to solving systems of subtype inequalities. We consider simple types ordered structurally from an arbitrary set of base subtype assumptions. In this case, we give a PSPACE upper bound. Together with the known lower bound, this result settles completely the complexity of type inference ov...

We present a new and simple approach to concentration inequalities for functions around their expectation with respect to non-product measures, i.e., for dependent random variables. Our method is based on coupling ideas and does not use information inequalities. When one has a uniform control on the coupling, this leads to exponential concentration inequalities. When such a uniform control is n...