计算几何与并行算法

本文首先介绍了计算几何的基本概念,论述了计算几何的四个基本问题,即几何搜索问题、相交问题、邻接问题及凸壳问题。然后重点分析了凸壳构造问题,介绍了其最佳串行算法、及相应的并行算法。接着对一些计算几何的串行及并行算法进行了分析比较。最后提出了笔者对新一代并行计算机系统上设计计算几何并行算法的看法。     

VLSI systems for some problems of computational geometry

Fast solution of the computational geometry problems is important for computer graphics, image processing and pattern recognition. The capability of the network Mesh of Trees for application in VLSI systems solving fastly the computational geometry problems is shown on two examples: determination of the convex hull of a weakly externally visible polygon and determination of the visibility polygon of a polygon.     

A method for particle location and field interpolation on complex, three-dimensional computational meshes

A method for locating particles within arbitrary three-dimensional computational meshes is described. It is based on an iterative procedure which uses transformed coordinates defined by iso-parametric functions. The method also enables one to interpolate field values from the mesh nodes to the particle position. Example applications demonstrate how effective the method is. For very distorted computational cells special practices have to be introduced in order to keep the number of iterations to a minimum.     

Parallel finding all initial palindromes and periods of a string on reconfigurable meshes

Given a string of lengthn, this short paper first presents anO(1)-time parallel algorithm for finding all initial palindromes and periods of the string on ann×n reconfigurable mesh (RM). Then, under the same cost (= time × the number of processors =O(n ²)), we provide a partitionable strategy when the RM doesn’t offer sufficient processors; this overcomes the hardware limitation and is very suitable for VLSI implementation. Prof. Chung was supported in part by the National Science Council of R. O. C. under contracts NSC87-2213-E011-001 and NSC87-2213-E011-003.