Related papers: Integer Programming with GCD Constraints

We give an exact algorithm for the 0-1 Integer Linear Programming problem with a linear number of constraints that improves over exhaustive search by an exponential factor. Specifically, our algorithm runs in time…

We study integer programming instances over polytopes P(A,b)={x:Ax<=b} where the constraint matrix A is random, i.e., its entries are i.i.d. Gaussian or, more generally, its rows are i.i.d. from a spherically symmetric distribution. The…

Finding the largest code with a given minimum distance is one of the most basic problems in coding theory. In this paper, we study the linear programming bound for codes in the Lee metric. We introduce refinements on the linear programming…

This paper studies the computational complexity of a robust variant of a two-stage submodular minimization problem that we call Robust Submodular Minimizer. In this problem, we are given $k$ submodular functions~$f_1,\dots,f_k$ over a set…

Let $\{\phi_p\}$ be an optimal G\"odel numbering of the family of computable functions (in Schnorr's sense), where $p$ ranges over binary strings. Assume that a list of strings $L(p)$ is computable from $p$ and for all $p$ contains a…

We analyze integer linear programs which we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness…

In this paper, we will show that the width of simplices defined by systems of linear inequalities can be computed in polynomial time if some minors of their constraint matrices are bounded. Additionally, we present some…

Let $F \in \R[X_1,\ldots,X_n]$ and the zero set $V=\zero(\mathcal{P},\R^n)$, where $\mathcal{P}:=\{P_1,\ldots,P_s\} \subset \R[X_1,\ldots,X_n]$ is a finite set of polynomials. We investigate existence of critical points of $F$ on an…

This paper describes an approximate method for global optimization of polynomial programming problems with bounded variables. The method uses a reformulation and linearization technique to transform the original polynomial optimization…

A rational number is dyadic if it has a finite binary representation $p/2^k$, where $p$ is an integer and $k$ is a nonnegative integer. Dyadic rationals are important for numerical computations because they have an exact representation in…

Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…

We consider the integer Chebyshev problem, that of minimizing the supremum norm over polynomials with integer coefficients on the interval $[0,1]$. We implement algorithms from semi-infinite programming and a branch and bound algorithm to…

Two models were recently proposed to explore the robust hardness of Gr\"obner basis computation. Given a polynomial system, both models allow an algorithm to selectively ignore some of the polynomials: the algorithm is only responsible for…

This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…

Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…

We prove new cases of reasonable bounds for the polynomial Szemer\'{e}di theorem both over $\mathbb{Z}/N\mathbb{Z}$ with $N$ prime and over the integers. In particular, we prove reasonable bounds for Szemer\'edi's theorem in the integers…

We describe how to compute for two polynomials $f(X), g(X) \in \mathbb{Z}[X]$ with integer coefficients the greatest common divisors of $f(z)$ and $g(z)$ for all integers $z \in \mathbb{Z}$. As an application we determine the structures…

Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…

The minimum common string partition problem is an NP-hard combinatorial optimization problem with applications in computational biology. In this work we propose the first integer linear programming model for solving this problem. Moreover,…

We investigate the question whether Subset Sum can be solved by a polynomial-time algorithm with access to a certificate of length poly(k) where k is the maximal number of bits in an input number. In other words, can it be solved using only…