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Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
This paper focuses on integer linear programs where solutions are binary matrices, and the corresponding symmetry group is the set of all column permutations. Orbitopal fixing, as introduced by Kaibel et al., is a technique designed to…
This paper studies the problem of enumerating all maximal collinear subsets of size at least three in a given set of $n$ points. An algorithm for this problem, besides solving degeneracy testing and the exact fitting problem, can also help…
A bottleneck plane perfect matching of a set of $n$ points in $\mathbb{R}^2$ is defined to be a perfect non-crossing matching that minimizes the length of the longest edge; the length of this longest edge is known as {\em bottleneck}. The…
Let $k\ge 1$ be an integer, and let $P= (f_1(x), \ldots, f_k(x) )$ be $k$ admissible linear polynomials over the integers, or \textit{the pattern}. We present two algorithms that find all integers $x$ where $\max{ \{f_i(x) \} } \le n$ and…
The balanced incomplete block design (BIBD) problem is a difficult combinatorial problem with a large number of symmetries, which add complexity to its resolution. In this paper, we propose a dual (integer) problem representation that…
We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed diagonal gate and an arbitrary gate. These sequences are…
Motivated by the expressive power of completely positive programming to encode hard optimization problems, many approximation schemes for the completely positive cone have been proposed and successfully used. Most schemes are based on outer…
In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as flows in suitable matrix spaces, which in turn leads to the…
The hypercube queueing model was initially developed to address spatial queueing problems and has found wide applications in emergency services, such as ambulance and police systems. While the model was originally designed for homogeneous…
We propose a novel physical realization of a quantum computer. The qubits are electric dipole moments of ultracold diatomic molecules, oriented along or against an external electric field. Individual molecules are held in a 1-D trap array,…
Motif finding is one of the NP-complete problems in Computational Biology. Existing nondeterministic algorithms for motif finding do not guarantee the global optimality of results and are sensitive to initial parameters. To address this…
The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…
A perfect (Delaunay) ellipsoid is an ellipsoid in n-dimensional Euclidean space that does not contain integral points in its interior, but is uniquely defined by integral points that lie on its surface. A perfect Delaunay polytope with…
Graph modification problems, which aim to find a small set of modifications to a graph so that it satisfies a desired property, have been studied for several special graph classes. The literature is rather rich in NP-completeness results…
An effective upper bound is established for the least non-trivial integer solution to the system of cubic forms \[ \begin{cases} F = c_{1}x_1^3 + c_{2}x_2^3 + \cdots + c_{n}x_n^3 = 0, \\ G = d_{1}x_1^3 + d_{2}x_2^3 + \cdots + d_{n}x_n^3 =…
We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…
Solving non-linear Diophantine systems lies at the mathematical core of integer optimization and cryptography. While the general unbounded problem is undecidable, even over bounded integer domains it remains classically intractable in the…
On modern architectures, the performance of 32-bit operations is often at least twice as fast as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating point arithmetic, the performance of many dense and…
In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on…