In this paper we describe a new method of position detection for a mesh-backed printing screen with an alignment mark that is overlapped by mesh patterns. A circular hole is selected as an alignment mark so that at least a portion of its contour can be observed through the windows of the mesh wires. To recognize the true contour, the smallest circle enclosing binary patterns acquired with a tra...

We consider a group of mobile robotic agents, identical and indistinguishable, having no memory (oblivious) and no common frame of reference (neither absolute location nor a common orientation). Furthermore, these agents are assumed to posses only rudimentary sensing and computational capabilities (limited visibility and basic geometric sorting). We prove that, such robots, implementing a ”Chas...

Clustering algorithms are routinely used in biomedical disciplines, and are a basic tool in bioinformatics. Depending on the task at hand, there are two most popular options, the central partitional techniques and the Agglomerative Hierarchical Clustering techniques and their derivatives. These methods are well studied and well established. However, both categories have some drawbacks related t...

We systematically investigate the farthest distance function, farthest points, Klee sets, and Chebyshev centers, with respect to Bregman distances induced by Legendre functions. These objects are of considerable interest in Information Geometry and Machine Learning; when the Legendre function is specialized to the energy, one obtains classical notions from Approximation Theory and Convex Analys...

We show the power of posets in computational geometry by solving several problems posed on a set S of n points in the plane: (1) nd the n ? k ? 1 rectilinear farthest neighbors (or, equivalently, k nearest neighbors) to every point of S (extendable to higher dimensions), (2) enumerate the k largest (smallest) rectilinear distances in decreasing (increasing) order among the points of S, (3) give...

We investigate higher-order Voronoi diagrams in the city metric. This metric is induced by quickest paths in the L1 metric in the presence of an accelerating transportation network of axis-parallel line segments. For the structural complexity of k-order city Voronoi diagrams of n point sites, we show an upper bound of O(k(n − k) + kc) and a lower bound of Ω(n+ kc), where c is the complexity of ...