Podality-based time-optimal computations on enhanced meshes

Abstract

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 e, all instances of size m, n m n 1 2 + £ £ e e j of the problems above, stored in the first m n columns of a mesh with multiple broadcasting of size n n ¥ can be solved time-optimally in Q m n e j time.

Full Binary Tree-Based Fixed Degree Graph Design and Parallel Algorithm

“…[27] [28] [29]. To address the disadvantage of the star graph, several alternatives have been proposed, such as an alternating group [30], star-connected cycles graph [28], (n, k)-star graph [28], bubble-sort star graph [26], transposition graph [15] [31], and macro-star graph [32].…”

A Novel Interconnection Network with Improved Network Cost Through Shuffle-Exchange Permutation Graph

“…The mesh structure has been widely used as a planar graph to date, and commercialized in various systems [19,20]. An m-dimensional mesh M m (N) consists of N m nodes and mN m − mN m−1 edges.…”

“…The higher the dimension of a mesh, the smaller its diameter and the larger the bisection width, and various parallel algorithms can be rapidly executed; however, it is costly [6]. Structures that improve the diameter of a mesh with a typical lattice structure, hexagonal mesh, toroidal mesh, diagonal mesh, honeycomb mesh, and torus have been proposed [19,21].…”

One-to-One Embedding between Honeycomb Mesh and Petersen-Torus Networks

“…Since a low dimension mesh can be readily designed and is very useful in terms of algorithm, it is frequently used as interconnection network for parallel computers. The higher the dimensions of the mesh are, the shorter is diameter and the larger is bisection width and several parallel algorithms can be rapidly performed, but it requires a huge cost [ 15 ]. Honeycomb mesh is proposed as an interconnection network, which is characterized by more economic network cost, better location of mobile base station, and application fields such as computer graphic, image processing etc.…”