Mesh Connected Computers With Multiple Fixed Buses: Packet Routing, Sorting and Selection

Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing, sorting, and selection on these models. In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k-k routing, k-k sorting, and cut through routing on a 2D mesh for any k ≥ 12. We provide an improved algorithm for 1-1 routing and a matching sorting algorithm. In addition we present greedy algorithms for 1-1 routing, k-k routing, cut through routing, and k-k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed in logarithmic time on a mesh with fixed buses. As a consequence we present an optimal randomized selection algorithm. In addition we provide a selection algorithm for the mesh with reconfigurable buses whose time bound is significantly better than the existing ones. Our algorithms have considerably better time bounds than many existing best known algorithms

Randomized Routing and Sorting on the Reconfigurable Mesh

In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer (referred to simply as the mesh from hereon). The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. In particular, we show that permutation routing problem can be solved on a linear array of size n in 3/4n steps, whereas n-1 is the best possible run time without reconfiguration. We also show that permutation routing on an n x n reconfigurable mesh can be done in time n + o(n)using a randomized algorithm or in time 1.25n + o(n) deterministically. In contrast, 2n-2 is the diameter of a conventional mesh and hence routing and sorting will need at least 2n-2 steps on a conventional mesh. In addition we show that the problem of sorting can be solved in time n+ o(n). All these time bounds hold with high probability. The bisection lower bound for both sorting and routing on the mesh is n/2, and hence our algorithms have nearly optimal time bounds

High Performance Issues in Image Processing and Computer Vision

Typical image processing and computer vision tasks found in industrial, medical, and military applications require real-time solutions. These requirements have motivated the design of many parallel architectures and algorithms. Recently, a new architecture called the reconfigurable mesh has been proposed. This thesis addresses a number of problems in image processing and computer vision on reconfigurable meshes. We first show that a number of low-level descriptors of a digitized image such as the perimeter, area, histogram and median row can be reduced to computing the sum of all the integers in a matrix, which in turn can be reduced to computing the prefix sums of a binary sequence and the prefix sums of an integer sequence. We then propose a new computational paradigm for reconfigurable meshes, that is, identifying an entity by a bus and performing computations on the bus to obtain properties of the entity. Using the new paradigm, we solve a number of mid-level vision tasks including the Hough transform and component labeling. Finally, a VLSI-optimal constant time algorithm for computing the convex hull of a set of planar points is presented based on a VLSI-optimal constant time sorting algorithm. As by-products, two basic data movement techniques, computing the prefix sums of a binary sequence and computing the prefix maxima of a sequence of real numbers, and a VLSI-optimal constant time sorting algorithm have been developed. These by-products are interesting in their own right. In addition, they can be exploited to obtain efficient algorithms for a number of computational problems

Adaptive AT2 Optimal Algorithms on reconfigurable meshes

Recently a few self-simulation algorithms have been developed to execute algorithms on a reconfigurable mesh (RM) of size smaller than recommended in those algorithms. Optimal slowdown, in self-simulation, has been achieved with the compromise that the resultant algorithms fail to remain AT2 optimal. In this paper we have introduced, for the first time, the idea of adaptive algorithm which runs on RM of variable sizes without compromising the AT2 optimality. We have supported our idea by developing adaptive algorithms, for sorting items and computing the contour of maximal elements of a set of planar points on RM. We have also conjectured that to obtain an AT2 algorithm to solve a problem of size n with I(n) information content on an RM of size p x q where pq=kI(n), it is sufficient to form buses of length O (k)

Visibility-Related Problems on Parallel Computational Models

Visibility-related problems find applications in seemingly unrelated and diverse fields such as computer graphics, scene analysis, robotics and VLSI design. While there are common threads running through these problems, most existing solutions do not exploit these commonalities. With this in mind, this thesis identifies these common threads and provides a unified approach to solve these problems and develops solutions that can be viewed as template algorithms for an abstract computational model. A template algorithm provides an architecture independent solution for a problem, from which solutions can be generated for diverse computational models. In particular, the template algorithms presented in this work lead to optimal solutions to various visibility-related problems on fine-grain mesh connected computers such as meshes with multiple broadcasting and reconfigurable meshes, and also on coarse-grain multicomputers. Visibility-related problems studied in this thesis can be broadly classified into Object Visibility and Triangulation problems. To demonstrate the practical relevance of these algorithms, two of the fundamental template algorithms identified as powerful tools in almost every algorithm designed in this work were implemented on an IBM-SP2. The code was developed in the C language, using MPI, and can easily be ported to many commercially available parallel computers

An efficient parallel algorithm for the all pairs shortest path problem using processor arrays with reconfigurable bus systems

The all pairs shortest path problem is a class of the algebraic path problem. Many parallel algorithms for the solution of this problem appear in the literature. One of the efficient parallel algorithms on W-RAM model is given by Kucera [17]. Though efficient, algorithms written for the W-RAM model of parallel computation are too idealistic to be implemented on the current hardware. In this report we present an efficient parallel algorithm for the solution of this problem using a relatively new model of parallel computing, Processor Arrays with Reconfigurable Bus Systems. The parallel time complexity of this algorithm is O(log2 n) and processors complexity is n2 × n × n

A fast parallel algorithm for special linear systems of equations using processor arrays with reconfigurable bus systems

A parallel algorithm using Processor Arrays with Reconfigurable Bus Systems has been designed to solve dense Symmetric Positive Definite (SPD) systems of equations Ax = b. The key content of this report is the parallelisation of the algorithm by Delosme & Ipson [8]. In order to design a parallel algorithm for PARBS, many procedures involved in [8] are handled in a slightly different way. The parallel time and processor’s complexity of each step of the algorithm is calculated. The parallel time complexity is O(n) using 2n × 2n × 5n number of Processing Elements

Efficient parallel computation on multiprocessors with optical interconnection networks

This dissertation studies optical interconnection networks, their architecture, address schemes, and computation and communication capabilities. We focus on a simple but powerful optical interconnection network model - the Linear Array with Reconfigurable pipelined Bus System (LARPBS). We extend the LARPBS model to a simplified higher dimensional LAPRBS and provide a set of basic computation operations. We then study the following two groups of parallel computation problems on both one dimensional LARPBS\u27s as well as multi-dimensional LARPBS\u27s: parallel comparison problems, including sorting, merging, and selection; Boolean matrix multiplication, transitive closure and their applications to connected component problems. We implement an optimal sorting algorithm on an n-processor LARPBS. With this optimal sorting algorithm at disposal, we study the sorting problem for higher dimensional LARPBS\u27s and obtain the following results: • An optimal basic Columnsort algorithm on a 2D LARPBS. • Two optimal two-way merge sort algorithms on a 2D LARPBS. • An optimal multi-way merge sorting algorithm on a 2D LARPBS. • An optimal generalized column sort algorithm on a 2D LARPBS. • An optimal generalized column sort algorithm on a 3D LARPBS. • An optimal 5-phase sorting algorithm on a 3D LARPBS. Results for selection problems are as follows: • A constant time maximum-finding algorithm on an LARPBS. • An optimal maximum-finding algorithm on an LARPBS. • An O((log log n)2) time parallel selection algorithm on an LARPBS. • An O(k(log log n)2) time parallel multi-selection algorithm on an LARPBS. While studying the computation and communication properties of the LARPBS model, we find Boolean matrix multiplication and its applications to the graph are another set of problem that can be solved efficiently on the LARPBS. Following is a list of results we have obtained in this area. • A constant time Boolean matrix multiplication algorithm. • An O(log n)-time transitive closure algorithm. • An O(log n)-time connected components algorithm. • An O(log n)-time strongly connected components algorithm. The results provided in this dissertation show the strong computation and communication power of optical interconnection networks

Routing with locality in partitioned-bus meshes

We show that adding partitioned-buses (as opposed to long buses that span an entire row or column) to ordinary meshes can reduce the routing time by approximately one-third for permutation routing with locality. A matching time lower bound is also proved. The result can be generalized to multi-packet routing.published_or_final_versio

RMESH Algorithms for Parallel String Matching

String matching problem received much attention over the years due to its importance in various applications such as text/file comparison, DNA sequencing, search engines, and spelling correction. Especially with the introduction of search engines dealing with tremendous amount of textual information presented on the world wide web and the research on DNA sequencing, this problem deserves special attention and any algorithmic or hardware improvements to speed up the process will benefit these important applications. In this paper, we present three algorithms for string matching on reconfigurable mesh architectures. Given a text T of length n and a pattern P of length m, the first algorithm finds the exact matching between T and P in O(1) time on a 2-dimensional RMESH of size (n-m+1) * m. The second algorithm finds the approximate matching between T and P in O(k) time on a 2D RMESH, where k is the maximum edit distance between T and P. The third algorithm allows only the replacement operation in the calculation of the edit distance and finds an approximate matching between T and P in constant-time on a 3D RMESH