Related papers: Integer Programming and m-irreducibility of numeri…
In this paper we analyze the irreducibility of numerical semigroups with multiplicity up to four. Our approach uses the notion of Kunz-coordinates vector of a numerical semigroup recently introduced in (Blanco-Puerto, 2011). With this tool…
In this paper we introduce the notion of m-irreducibility that extends the standard concept of irreducibility of a numerical semigroup when the multiplicity is fixed. We analyze the structure of the set of m-irreducible numerical…
The intention of this note is two-fold. First, we study integer optimization problems in standard form defined by $A \in\mathbb{Z}^{m\times{}n}$ and present an algorithm to solve such problems in polynomial-time provided that both the…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
The minimum k-partition problem is a challenging combinatorial problem with a diverse set of applications ranging from telecommunications to sports scheduling. It generalizes the max-cut problem and has been extensively studied since the…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…
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…
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…
Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…
Integer linear programs $\min\{c^T x : A x = b, x \in \mathbb{Z}^n_{\ge 0}\}$, where $A \in \mathbb{Z}^{m \times n}$, $b \in \mathbb{Z}^m$, and $c \in \mathbb{Z}^n$, can be solved in pseudopolynomial time for any fixed number of constraints…
It is a notorious open question whether integer programs (IPs), with an integer coefficient matrix $M$ whose subdeterminants are all bounded by a constant $\Delta$ in absolute value, can be solved in polynomial time. We answer this question…
Numerical semigroups with multiplicity $m$ are parameterized by integer points in a polyhedral cone $C_m$, according to Kunz. For the toric ideal of any such semigroup, the main result here constructs a free resolution whose overall…
We complete the complexity classification by degree of minimizing a polynomial over the integer points in a polyhedron in $\mathbb{R}^2$. Previous work shows that optimizing a quadratic polynomial over the integer points in a polyhedral…
Mixed integer predictive control deals with optimizing integer and real control variables over a receding horizon. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
In this paper we present a mathematical formulation for the omega invariant of a numerical semigroup for each of its minimal generators. The model consists of solving a problem of optimizing a linear function over the efficient set of a…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…
Quantum computers promise to outperform their classical counterparts at certain tasks. However, existing quantum devices are error-prone and restricted in size. Thus, effective compilation methods are crucial to exploit limited quantum…
We introduce a new class of optimization problems called integer Minkowski programs. The formulation of such problems involves finitely many integer variables and nonlinear constraints involving functionals defined on families of discrete…