Let (QP ) be an integer quadratic program that consists in minimizing a quadratic function subject to linear constraints. In this paper, we present several linearizations of (QP ). Many linearization methods for the quadratic 0-1 programs are known. A natural approach when considering (QP ) is to reformulate it into a quadratic 0-1 program. However, this method, that we denote BBL (Binary Binar...

Abstract An arbitrary starting variable dimension algorithm is developed for computing an integer point of a polytope, P = {x | Ax ≤ b}, which satisfies that each row of A has at most one positive entry. The algorithm is derived from an integer labelling rule and a triangulation of the space. It consists of two phases, one of which forms a variable dimension algorithm and the other a full-dimen...

In this paper, we propose a sophisticated technique of data dependence analysis for distributed memory parallel environments that is used for converting sequential code into a parallel form targeted for a particular architecture. Two-dimensional arrays with subscripts formed by induction variable in real programs appear quite frequently [10]. We test if there are integervalued solutions for two...

a mapping $f:v^n longrightarrow w$, where $v$ is a commutative semigroup, $w$ is a linear space and $n$ is a positive integer, is called multi-additive if it is additive in each variable. in this paper we prove the hyers-ulam stability of multi-additive mappings in 2-banach spaces. the corollaries from our main results correct some outcomes from [w.-g. park, approximate additive mappings i...

The simple integer recourse (SIR) function of a decision variable is the expectation of the integer roundup of the shortage/surplus between a random variable with a known distribution and the decision variable. It is the integer analogue of the simple (continuous) recourse function in two stage stochastic linear programming. Structural properties and approximations of SIR functions have been ex...

A survey of results for Mahler measure of algebraic numbers, and one-variable polynomials with integer coefficients is presented. Related results on the maximum modulus of the conjugates (‘house’) of an algebraic integer are also discussed. Some generalisations are also mentioned, though not to Mahler measure of polynomials in more than one variable.

In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N , these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any c...

Given an instance of Weighted Vertex Cover, we can encode it as an integer programming (IP) problem. Create a 0/1 indicator variable xv for each vertex v ∈ V : xv = 1 indicates v is in the cover; xv = 0 otherwise. We force {v : xv = 1} to be a cover by requiring that for each edge {u, v} ∈ E, xu = 1 or xv = 1 (or equivalently, xu + xv ≥ 1). Finally, since our objective is to find a minimum-cost...