Related papers: A Simple Circle Discretization Algorithm With Appl…
In this paper, we study the problem of finding the Euclidean distance to a convex cone generated by a set of discrete points in $\mathbb{R}^n_+$. In particular, we are interested in problems where the discrete points are the set of feasible…
This paper addresses the numerical computation of critical angles between two convex cones in finite-dimensional Euclidean spaces. We present a novel approach to computing these critical angles by reducing the problem to finding stationary…
Cluster deletion is an NP-hard graph clustering objective with applications in computational biology and social network analysis, where the goal is to delete a minimum number of edges to partition a graph into cliques. We first provide a…
Iterative numerical algorithms are typically equipped with a stopping criterion, where the iteration process is terminated when some error or misfit measure is deemed to be below a given tolerance. This is a useful setting for comparing…
We propose new algebraic methods for extracting cylinders and cones from minimal point sets, including oriented points. More precisely, we are interested in computing efficiently cylinders through a set of three points, one of them being…
Sparse grids are tailored to the approximation of smooth high-dimensional functions. On a $d$-dimensional tensor product space, the number of grid points is $N = \mathcal O(h^{-1} |\log h|^{d-1})$, where $h$ is a mesh parameter. The…
In this paper, we present a cluster algorithm for the simulation of hard spheres and related systems. In this algorithm, a copy of the configuration is rotated with respect to a randomly chosen pivot point. The two systems are then…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
Clustering is a well-known and important problem with numerous applications. The graph-based model is one of the typical cluster models. In the graph model, clusters are generally defined as cliques. However, such an approach might be too…
Line intersection with convex and un-convex polygons or polyhedron algorithms are well known as line clipping algorithms and very often used in computer graphics. Rendering of geometrical problems often leads to ray tracing techniques, when…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…
Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach to constructing cyclic codes is the sequence approach. In…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…
We describe a new method to map the requested error tolerance on an H-matrix approximation to the block error tolerances. Numerical experiments show that the method produces more efficient approximations than the standard method for kernels…
Writing correct distributed programs is hard. In spite of extensive testing and debugging, software faults persist even in commercial grade software. Many distributed systems, especially those employed in safety-critical environments,…
We study algorithmic applications of a natural discretization for the hard-sphere model and the Widom-Rowlinson model in a region $\mathbb{V}\subset\mathbb{R}^d$. These models are used in statistical physics to describe mixtures of one or…
Cylindrical coordinates are often used in computational fluid dynamics, in particular, when one considers gas flow accreting onto a central object. Although the cylindrical coordinates have several advantages in describing rotation, they…
We study geometric variations of the discriminating code problem. In the \emph{discrete version} of the problem, a finite set of points $P$ and a finite set of objects $S$ are given in $\mathbb{R}^d$. The objective is to choose a subset…
In this work, a 2D contour generation algorithm is proposed for irregular regions. The contour of the physical domain is approximated by mesh segments using the known coordinates of the contour. For this purpose, the algorithm uses a…
Measuring software complexity plays an important role to meet the demands of complex software. The cyclomatic complexity is one of most used and renowned metric among the other three proposed and researched metrics that are namely: Line of…