Podality-Based Time-Optimal Computations on Enhanced Meshes

• Authors: Venkatavasu Bokka;Himabindu Gurla;Stephan Olariu;James L. Schwing
• Venue: IEEE Transactions on Parallel and Distributed Systems
• Year: 1997

The main contribution of this paper is to present simple and elegant podality-based algorithms for a variety of computational tasks motivated by, and finding applications to, pattern recognition, computer graphics, computational morphology, image processing, robotics, computer vision, and VLSI design. The problems that we address involve computing the convex hull, the diameter, the width, and the smallest area enclosing rectangle of a set of points in the plane, as well as the problems of finding the maximum Euclidian distance between two planar sets of points, and of constructing the Minkowski sum of two convex polygons. Specifically, we show that once we fix a positive constant $\epsilon,$ all instances of size m, $\left( {n^{{\textstyle{1 \over 2}}+\epsilon}\le m\le n} \right)$ of the problems above, stored in the first $\left\lceil {{\textstyle{m \over {\sqrt n}}}} \right\rceil $ columns of a mesh with multiple broadcasting of size $\sqrt n\times \sqrt n$ can be solved time-optimally in $\Theta \left( {{\textstyle{m \over {\sqrt n}}}} \right)$ time.