On the average running time of odd-even merge sort

This paper is concerned with the average running time of Batcher's odd-even merge sort when implemented on a collection of processors. We consider the case where $n$, the size of the input, is an arbitrary multiple of the number $p$ of processors used. We show that Batcher's odd-even merge (for two sorted lists of length $n$ each) can be implemented to run in time $O((n/p)(\log (2+p^2/n)))$ on the average, and that odd-even merge sort can be implemented to run in time $O((n/p)(\log n+\log p\log (2+p^2/n)))$ on the average. In the case of merging (sorting), the average is taken over all possible outcomes of the merging (all possible permutations of $n$ elements). That means that odd-even merge and odd-even merge sort have an optimal average running time if $n\geq p^2$. The constants involved are also quite small

A taxonomy of parallel sorting

TR 84-601In this paper, we propose a taxonomy of parallel sorting that includes a broad range of array and file sorting algorithms. We analyze the evolution of research on parallel sorting, from the earliest sorting networks to the shared memory algorithms and the VLSI sorters. In the context of sorting networks, we describe two fundamental parallel merging schemes - the odd-even and the bitonic merge. Sorting algorithms have been derived from these merging algorithms for parallel computers where processors communicate through interconnection networks such as the perfect shuffle, the mesh and a number of other sparse networks. After describing the network sorting algorithms, we show that, with a shared memory model of parallel computation, faster algorithms have been derived from parallel enumeration sorting schemes, where keys are first ranked and then rearranged according to their rank

Parallel Computation on Hypercube-Like Machines.

The hypercube interconnection network has been recognized to be very suitable for a parallel computing architecture due to its attractive topological properties. Recently, several modified hypercubes have been propose to improve the performance of a hypercube. This dissertation deals with two modified hypercubes, the X-hypercube and the Z-cube. The X-hypercube is a variant of the hypercube, with the same amount of hardware but a diameter of only $\lceil$(n + 1)/2$\rceil$ in a hypercube of dimension n. The Z-cube has only 75 percent of the edges of a hypercube with the same number vertices and the same diameter as the hypercube. In this dissertation, we investigate some topological properties and the effectiveness of the X-hypercube and the Z-cube in their combinatorial and computational aspects. We give the optimal or nearly optimal data communication algorithms including routing, broadcasting, and census function for the X-hypercube and the Z-cube. We also give the optimal embedding algorithms between the X-hypercube and the hypercube. It is shown that the average distance between vertices in a X-hypercube is roughly 13/16 of that in a hypercube. This implies that a X-hypercube achieves the better average communication performance than a hypercube. In addition, a set of fundamental SIMD algorithms for a X-hypercube is given. Our results indicate that the X-hypercube makes an improvement in performance over the hypercube, but not as much as the reduction in a diameter, and the Z-cube is a good alternative for the hypercube as far as the VLSI implementation is of major concern

New Techniques in Scene Understanding and Parallel Image Processing.

There has been tremendous research interest in the areas of computer and robotic vision. Scene understanding and parallel image processing are important paradigms in computer vision. New techniques are presented to solve some of the problems in these paradigms. Automatic interpretation of features in a natural scene is the focus of the first part of the dissertation. The proposed interpretation technique consists of a context dependent feature labeling algorithm using non linear probabilistic relaxation, and an expert system. Traditionally, the output of the labeling is analyzed, and then recognized by a high level interpreter. In this new approach, the knowledge about the scene is utilized to resolve the inconsistencies introduced by the labeling algorithm. A feature labeling system based on this hybrid technique is designed and developed. The labeling system plays a vital role in the development of an automatic image interpretation system for oceanographic satellite images. An extensive study on the existing interpretation techniques has been made in the related areas such as remote sensing, medical diagnosis, astronomy, and oceanography and has shown that our hybrid approach is unique and powerful. The second part of the dissertation presents the results in the area of parallel image processing. A new approach for parallelizing vision tasks in the low and intermediate levels is introduced. The technique utilizes schemes to embed the inherent data or computational structure, used to solve the problem, into parallel architectures such as hypercubes. The important characteristic of the technique is that the adjacent pixels in the image are mapped to nodes that are at a constant distance in the hypercube. Using the technique, parallel algorithms for neighbor-finding and digital distances are developed. A parallel hypercube sorting algorithm is obtained as an illustration of the technique. The research in developing these embedding algorithms has paved the way for efficient reconfiguration algorithms for hypercube architectures

Parallel alogorithms for MIMD parallel computers

This thesis mainly covers the design and analysis of asynchronous parallel algorithms that can be run on MIMD (Multiple Instruction Multiple Data) parallel computers, in particular the NEPTUNE system at Loughborough University. Initially the fundamentals of parallel computer architectures are introduced with different parallel architectures being described and compared. The principles of parallel programming and the design of parallel algorithms are also outlined. Also the main characteristics of the 4 processor MIMD NEPTUNE system are presented, and performance indicators, i.e. the speed-up and the efficiency factors are defined for the measurement of parallelism in a given system. Both numerical and non-numerical algorithms are covered in the thesis. In the numerical solution of partial differential equations, a new parallel 9-point block iterative method is developed. Here, the organization of the blocks is done in such a way that each process contains its own group of 9 points on the network, therefore, they can be run in parallel. The parallel implementation of both 9-point and 4- point block iterative methods were programmed using natural and redblack ordering with synchronous and asynchronous approaches. The results obtained for these different implementations were compared and analysed. Next the parallel version of the A.G.E. (Alternating Group Explicit) method is developed in which the explicit nature of the difference equation is revealed and exploited when applied to derive the solution of both linear and non-linear 2-point boundary value problems. Two strategies have been used in the implementation of the parallel A.G.E. method using the synchronous and asynchronous approaches. The results from these implementations were compared. Also for comparison reasons the results obtained from the parallel A.G.E. were compared with the ~ corresponding results obtained from the parallel versions of the Jacobi, Gauss-Seidel and S.O.R. methods. Finally, a computational complexity analysis of the parallel A.G.E. algorithms is included. In the area of non-numeric algorithms, the problems of sorting and searching were studied. The sorting methods which were investigated was the shell and the digit sort methods. with each method different parallel strategies and approaches were used and compared to find the best results which can be obtained on the parallel machine. In the searching methods, the sequential search algorithm in an unordered table and the binary search algorithms were investigated and implemented in parallel with a presentation of the results. Finally, a complexity analysis of these methods is presented. The thesis concludes with a chapter summarizing the main results

The connection machine

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1988.Bibliography: leaves 134-157.by William Daniel Hillis.Ph.D

Future Computer Requirements for Computational Aerodynamics

Recent advances in computational aerodynamics are discussed as well as motivations for and potential benefits of a National Aerodynamic Simulation Facility having the capability to solve fluid dynamic equations at speeds two to three orders of magnitude faster than presently possible with general computers. Two contracted efforts to define processor architectures for such a facility are summarized