Abstract: In this paper we propose a new approach to constructing the Delaunay Triangulation and the optimum algorithm for the case of multidimensional spaces (d ≥ 2). Analysing the modern state, it is possible to draw a conclusion, that the ideas for the existing effective algorithms developed for the case of d ≥ 2 are not simple to generalize on a multidimensional case, without the loss of efficiency. We offer for the solving this problem an effective algorithm that satisfies all the given requirements. But theoretical complexity of the problem it is impossible to improve as the Worst - Case Optimality for algorithms of solving such a problem is proved.
Abstract: We consider the methods of construction simple
polygons for a set S of n points and applying them for searching the
minimal area polygon. In this paper we propose the approximate
algorithm, which generates the simple polygonalizations of a fixed
set of points and finds the minimal area polygon, in O (n3) time and
using O(n2) memory.
Abstract: In this study we survey the method for fast finding a minimum link path between two arbitrary points within a simple polygon, which can pass only through the vertices, with preprocessing.