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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…
Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…
Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually…
A long-standing open question in Integer Programming is whether integer programs with constraint matrices with bounded subdeterminants are efficiently solvable. An important special case thereof are congruency-constrained integer programs…
Integer programs (IPs) on constraint matrices with bounded subdeterminants are conjectured to be solvable in polynomial time. We give a strongly polynomial time algorithm to solve IPs where the constraint matrix has bounded subdeterminants…
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…
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…
In this paper, a randomized algorithm for deciding the irreducibility of an irreducible polynomial and factoring a reducible polynomial over the field of rational numbers is presented. The main idea underlying the algorithm is based on…
This paper studies a strategy for data-driven algorithm design for large-scale combinatorial optimization problems that can leverage existing state-of-the-art solvers in general purpose ways. The goal is to arrive at new approaches that can…
We consider the semiring of abstract finite dynamical systems up to isomorphism, with the operations of alternative and synchronous execution. We continue searching for efficient algorithms for solving polynomial equations of the form $P(X)…
In this paper we study a new approach in optimization that aims to search a large domain D where a given function takes large, small or specific values via an iterative optimization algorithm based on the gradient. We show that the…
We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the…
In this thesis, I explore the possibilities of conducting Bayesian optimization techniques in high dimensional domains. Although high dimensional domains can be defined to be between hundreds and thousands of dimensions, we will primarily…
In this article, we give an account of some recent irreducibility testing criteria for polynomials having integer coefficients over the field of rational numbers.
We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of…
In this paper, a transform approach is used for polycyclic and serial codes over finite local rings in the case that the defining polynomials have no multiple roots. This allows us to study them in terms of linear algebra and invariant…
A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be…
We consider the following problem: Given a rational matrix $A \in \setQ^{m \times n}$ and a rational polyhedron $Q \subseteq\setR^{m+p}$, decide if for all vectors $b \in \setR^m$, for which there exists an integral $z \in \setZ^p$ such…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…
We give an elementary proof of a generalization of Bourgain and Tzafriri's Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which…