A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing [365] demonstrated that, in principle, a single general purpose sequential machine could be designed which would be capable of efficiently performing any computation which could be performed by a special purpose sequential machine. The importance of this universality result for subsequent practical developments in computing cannot be overstated. It showed that, for a given computational problem, the additional efficiency advantages which could be gained by designing a special purpose sequential machine for that problem would not be great. Around 1944, von Neumann produced a proposal [66, 389] for a general purpose storedprogram sequential computer which captured the fundamental principles of...

We survey routing problems on fixed-connection networks. We consider many aspects of the routing problem and provide known theoretical results for various communication models. We focus on (partial) permutation, k-relation routing, routing to random destinations, dynamic routing, isotonic routing, fault tolerant routing, and related sorting results. We also provide a list of unsolved problems and numerous references.

Introduction An mesh-connected multiprocessor array consists of identical processors M ×N M ×N i 1i M j ( positioned on a rectangular array. The processor located in row ( ) and column ) is referred to as . The mesh-connected architecture has emerged as one of t 1 j N P (i , j ) he most natural choices for solving a large number of computational tasks in image proi cessing, computational geometry, and computer vision. This is due, in part, to its simple nterconnection topology and to the fact that many problems feature data that maps easily - m onto the mesh structure. In addition, meshes are particularly well suited for VLSI imple entation [2,11,13]. However, due to their large communication diameter, meshes tend to be slow when it o comes to handling massive data transfer operations over long dista

We consider the following image processing problems: compute the area and perimeter of the components of an image, compute the histogram of an image, and histogram modification. Parallel reconfigurable mesh computer algorithms are developed for these problems. The area and perimeter of the components of an NN image are computed in O (logN) time by an NN RMESH; the histogram of an NN image is computed by an NN RMESH in O (min { B ), N}) time where B is the number of gray scale values; and histogram modification is done in O ( N ) time by an NN RMESH.

We consider the problems of selection, routing and sorting on an n-star graph (with n! nodes),an interconnection network which has been proven to possess many special properties. We identify a tree like subgraph (which we call as a ‘(k, 1,k) chain network’) of the star graph which enables us to design efficient algorithms for the above mentioned problems. We present an algorithm that performs a sequence of n prefix computations in O(n 2) time. This algorithm is used as a subroutine in our other algorithms. We also show that sorting can be performed on the n-star graph in time O(n 3) and that selection of a set of uniformly distributed n keys can be performed in O(n 2) time with high probability. Finally, we also present a deterministic (non oblivious) routing algorithm that realizes any permutation in O(n 3) steps on the n-star graph. There exists an algorithm in the literature that can perform a single prefix computation in O(n lg n) time. The best known previous algorithm for sorting has a run time of O(n 3 lg n) and is deterministic. To our knowledge, the problem of selection has not been considered before on the star graph. 1

. We present a strategy to develop, in a functional setting, correct, efficient and portable Divide-and-Conquer (DC) programs for massively parallel architectures. Starting from an operational DC program, mapping sequences to sequences, we apply a set of semantics preserving transformation rules, which transform the parallel control structure of DC into a sequential control flow, thereby making the implicit data parallelism in a DC scheme explicit. In the next phase of our strategy, the parallel architecture is fully expressed, where `architecture dependent' higher-order functions are introduced. Then -- due to the rising communication complexities on particular architectures -- topology dependent communication patterns are optimized in order to reduce the overall communication costs. The advantages of this approach are manifold and are demonstrated with a set of non-trivial examples. 1 Introduction It is well-known that the main problems in exploiting the power of modern parallel sys...

Our contribution is twofold. First, we show that \Omega\Gammaat/ n) is a time lower bound on the CREW-PRAM and the mesh with multiple broadcasting for the tasks of computing the perimeter, the area, the diameter, the width, the modality, the smallest-area enclosing rectangle, and the largest-area inscribed triangle of a convex n-gon. We show that the same time lower bound holds for the tasks of detecting whether a convex n-gon lies inside another as well as for computing the maximum distance between two convex n-gons. We obtain our time lower bound results for the CREW-PRAM by using a novel technique involving geometric constructions. These constructions allow us to reduce the well-known OR problem to each of the geometric problems of interest. We then port these time lower bounds to the mesh with multiple broadcasting using simulation results. Our second contribution is to show that the \Omega\Gammae/1 n) time lower bound is tight by providing O(log n) time algorithms to solve these p...

techniques allow severalprocessors within a multiprocessing

The {\em multisearch problem} is defined as follows. Given a data structure $D$ modeled as a graph with $n$ constant-degree nodes, perform $O(n)$ searches on $D$. Let $r$ be the length of the longest search path associated with a search process, and assume that the paths are determined ``on-line''. That is, the search paths may overlap arbitrarily. In this paper, we solve the multisearch problem for certain classes of graphs in $O(\sqrt{n} + {r} \frac{\sqrt{n}}{\log n})$ time on a $\sqrt{n} \times \sqrt{n}$ mesh-connected computer. For many data structures, the search path traversed when answering one search query has length $r=O(\log n)$. For these cases, our algorithm processes $O(n)$ such queries in asymptotically optimal $\Theta(\sqrt{n})$ time. The classes of graphs we consider contain many of the important data structures that arise in practice, ranging from simple trees to Kirkpatrick hierarchical search DAGs. Multisearch is a useful abstraction that can be used to implement parallel versions of standard sequential data structures on a mesh. As example applications, we consider a variety of parallel online tree traversals, as well as hierarchical representations of polyhedra and its myriad of applications (lines-polyhedron intersection queries, multiple tangent plane determination, intersecting convex polyhedra, and three-dimensional convex hull).

This paper provides an overview of lower and upper bounds for algorithms for mesh-connected processor networks. Most of our attention goes to routing and sorting problems, but other problems are mentioned as well. Results from 1977 to 1995 are covered. We provide numerous results, references and open problems. The text is completed with an index. This is a worked-out version of the author's contribution to a joint paper with Miltos D. Grammatikakis, D. Frank Hsu and Miro Kraetzl on multicomputer routing, submitted to the Journal of Parallel and Distributed Computing.