Related papers: On the Containment Problem for Linear Sets
Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…
Approximating a definite integral of product of cosines to within an accuracy of n binary digits where the integrand depends on input integers x[k] given in binary radix, is equivalent to counting the number of equal-sum partitions of the…
In this note, we prove that the problem of computing the linear discrepancy of a given matrix is $\Pi_2$-hard, even to approximate within $9/8 - \epsilon$ factor for any $\epsilon > 0$. This strengthens the NP-hardness result of Li and…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
We consider the problem of computing matrix polynomials $p(X)$, where $X$ is a large dense matrix, with as few matrix-matrix multiplications as possible. More precisely, let $\Pi_{2^{m}}^*$ represent the set of polynomials computable with…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
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 address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
The aim in packing problems is to decide if a given set of pieces can be placed inside a given container. A packing problem is defined by the types of pieces and containers to be handled, and the motions that are allowed to move the pieces.…
We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…
It is well known that, given \(b\ge 0\), finding an $(a,b)$-trapping set with the minimum \(a\) in a binary linear code is NP-hard. In this paper, we demonstrate that this problem can be solved with linear complexity with respect to the…
Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied…
Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…
We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations. We show the close connection between this problem and a…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
Motivated by problems of comparative genomics and paleogenomics, in [Chauve et al., 2009], the authors introduced the Gapped Consecutive-Ones Property Problem (k,delta)-C1P: given a binary matrix M and two integers k and delta, can the…
The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…
We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…
An uniform LP duality is an useful property of conic matrix systems. A consistent linear conic optimization problem yields uniform LP duality if for any linear cost function, for which the primal problem has finite optimal value, the…