Related papers: A Practical Approach for Computing the Diameter of…
We give an attempt to build a classification of planar integral point sets. For two obtained classes, we provide general constructions of upper bounds for minimal diameter of integral point sets in higher dimensions of certain cardinality.…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
We present a new algorithm, trimed, for obtaining the medoid of a set, that is the element of the set which minimises the mean distance to all other elements. The algorithm is shown to have, under certain assumptions, expected run time…
We refine the bit complexity analysis of an algorithm for the computation of at least one point per connected component of a smooth real algebraic set, yielding exponential speedup (with respect to the number of variables) compared to prior…
We present a novel method to compute the approximate global penetration depth (PD) between two non-convex geometric models. Our approach consists of two phases: offline precomputation and run-time queries. In the first phase, our…
Adders are key building blocks of many error-tolerant applications. Leveraging the application-level error tolerance, a number of approximate adders were proposed recently. Many of them belong to the category of block-based approximate…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
In 2012 Driemel et al. \cite{DBLP:journals/dcg/DriemelHW12} introduced the concept of $c$-packed curves as a realistic input model. In the case when $c$ is a constant they gave a near linear time $(1+\varepsilon)$-approximation algorithm…
In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove $\Delta$-convergence of the generated sequence to a critical point (which is defined in the text)…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
$\renewcommand{\Re}{\mathbb{R}}\newcommand{\eps}{{\varepsilon}}\newcommand{\poly}{\mathrm{poly}} $In this paper, we study the problem of $L_1$-fitting a shape to a set of $n$ points in $\Re^d$ (where $d$ is a fixed constant), where the…
In CNC manufacturing,there often arises the need to create G-Code programs which require the calculation of discrete x-y coordinate pairs(2D).An example of this situation is when the programmer needs to create a program to machine a…
We propose a new method for estimating the intrinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We propose a regularization scheme which is motivated by…
We present an algorithm for performing precise aperture photometry on critically sampled astrophysical images. The method is intended to overcome the small-aperture limitations imposed by point-sampling. Aperture fluxes are numerically…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…
We design an efficient data structure for computing a suitably defined approximate depth of any query point in the arrangement $\mathcal{A}(S)$ of a collection $S$ of $n$ halfplanes or triangles in the plane or of halfspaces or simplices in…
A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…