Reconfigurable Mesh Research Articles

Scaling simulation of the fusing-restricted reconfigurable mesh

This paper deals with the ability of a model to adapt algorithm instances of different sizes to run on a given model size without significant loss of efficiency. The overhead in simulating a step of a large instance of the model on a smaller instance can quantify this ability. A reconfigurable mesh (R-Mesh) can use its bus structure as a computational resource, presenting an obstacle to efficiently scaling down algorithms to run on a smaller R-Mesh. We construct a scaling simulation of a Fusing-Restricted Reconfigurable Mesh (FR-Mesh), a version of the R-Mesh. The overhead of this simulation depends only on the simulating machine size and not on the simulated machine size. Previously, the R-Mesh was not known to admit such a simulation overhead without significantly reducing its computational power. The small overhead holds importance for flexibility in algorithm design and for running algorithms with various input sizes on an available model of given size. The results of this paper extend to a variety of concurrent write rules and also translate to an improved scaling simulation of an unrestricted R-Mesh.

Visibility Computation on Reconfigurable Meshes

Visibility problems are investigated using reconfigurable meshes. A number of algorithms are proposed on the architecture for visibility computation in two and three dimensions. We show that visibility of a total of ndisjoint edges in the plane can be computed in O(1) time on an n× nmesh. The result is optimal in the word model of VLSI. For the case that the edges are not disjoint, the problem is shown to be solvable in O(1) time by using a mesh of slightly larger size or in slightly more time on an n× nmesh. We also present hidden-line and surface elimination algorithms that run on an n× n× nmesh for a set of disjoint triangles in 3-space containing a total of nvertices in O(1) time and O( k) time, respectively, where 0 ≤ k< nis an output-dependent parameter.

Constant Time Graph Algorithms on the Reconfigurable Multiple Bus Machine

The reconfigurable multiple bus machine (RMBM) is a model of parallel computation based on reconfigurable buses. Unlike other reconfigurable bus-based models such as the reconfigurable mesh (R-Mesh), the RMBM separates the functions of processors and switches. In this paper, we present constant time RMBM algorithms for a number of fundamental graph problems. These algorithms are more efficient, in terms of processors, than corresponding R-Mesh algorithms. Also presented is a novel range reduction technique for a constant time simulation of each step of a Priority CRCW RMBM on a Common or Collision CRCW RMBM. This simulation incurs only a factor ofO(Pϵ) increase in the number of processors and buses, where ϵ > 0 is any constant andPis the number of processors in the simulated Priority CRCW RMBM. This method may be of independent interest. The algorithms presented in this paper demonstrate the potential for fast and processor-efficient computation available in the ability of a reconfigurable bus-based model to separate the functions of processors and switches.

Simulating Shared Memory in Real Time: On the Computation Power of Reconfigurable Architectures

We consider randomized simulations of shared memory on a distributed memory machine (DMM) where the n processors and the n memory modules of the DMM are connected via a reconfigurable architecture. We first present a randomized simulation of a CRCW PRAM on a reconfigurable DMM having a complete reconfigurable interconnection. It guarantees delay O (log * n ), with high probability. Next we study a reconfigurable mesh DMM (RM-DMM). Here the n processors and n modules are connected via an n × n reconfigurable mesh. It was already known that an n × m reconfigurable mesh can simulate in constant time an n -processor CRCW PRAM with shared memory of size m . In this paper we present a randomized step by step simulation of a CRCW PRAM with arbitrarily large shared memory on an RM-DMM. It guarantees constant delay with high probability, i.e., it simulates in real time. Finally we prove a lower bound showing that size Ω ( n 2 ) for the reconfigurable mesh is necessary for real time simulations.

Time-Efficient Maze Routing Algorithms on Reconfigurable Mesh Architectures

The routing problem is one of the most widely studied problems in VLSI design. Maze-routing algorithms are used in VLSI routing and robot path planning. Efficiency of the parallel maze routing algorithms which were mostly based on C. Y. Lee's algorithm8is poor. In this paper, we propose time-efficient algorithms to solve the maze-routing problem on a reconfigurable mesh architecture. The constant-time algorithms presented include: (i) testing the existence of specific types of paths between two terminals, and (ii) finding an absolute shortest path (ASP) and a shortest duplex-path (SDP). In addition, a fast algorithm to find the single shortest path (SSP) is presented. The simulation results indicate that a large percentage of the shortest paths that exist between two randomly selected terminals fall into one of the categories studied in this paper.

A Scalable and Efficient Algorithm for Computing the City Block Distance Transform on Reconfigurable Meshes

The distance transform is a basic operation in computer vision, pattern recognition and robotics. In this paper, we consider the city block (L1) distance metric. An algorithm for computing the city block distance transform on reconfigurable meshes is proposed in this paper. The time complexity and scalability of the algorithm are analysed. The results indicate that the algorithm is scalable and efficient.

An optimal multiplication algorithm on reconfigurable mesh

An O(1) time algorithm to multiply two K-bit binary numbers using an N/spl times/N bit-model of reconfigurable mesh is shown. It uses optimal mesh size and it improves previously known results for multiplication on the reconfigurable mesh. The result is obtained by using novel techniques for data representation and data movement and using multidimensional Rader Transform. The algorithm is extended to result in AT/sup 2/ optimality over 1/spl les/t/spl les//spl radic/N in a variant of the bit-model of VLSI.

P-Bandwidth Priority Queues on Reconfigurable Tree of Meshes

This paper shows a parallel implementation of a priority queue with bandwidthPand maximum sizenPby means of a network with reconfigurable buses. The proposed solution is based on a tree of meshes architecture ofO(nP2) processors andO(Plogn) maximum subbus length. The computational times required by the operations of a priority queue with bandwidthPareO(1) for all the operations, using the unit-time delay model for broadcasting, while they areO(1) for MIN andO(logP+ log logn) for both DELETEMIN and INSERT, using the log-time delay model. The proposed network can be laid out in a classical H-shaped manner to occupyO(nP2) area in the VLSI model. WhenP=O(1), the required area is optimal and, using the unit-time delay model, the resultingAT2is also optimal. The paper presents also a very simple and efficient way of merging two sorted sequences on a reconfigurable mesh, which is used in the implementation of the priority queue operations.

Constant time algorithms for computational geometry on the reconfigurable mesh

The reconfigurable mesh consists of an array of processors interconnected by a reconfigurable bus system. The bus system can be used to dynamically obtain various interconnection patterns among the processors. Recently, this model has attracted a lot of attention. The authors show O(1) time solutions to the following computational geometry problems on the reconfigurable mesh: all-pairs nearest neighbors, convex hull, triangulation, two-dimensional maxima, two-set dominance counting, and smallest enclosing box. All these solutions accept N planar points as input and employ an N/spl times/N reconfigurable mesh. The basic scheme employed in the implementations is to recursively find an O(1) time solution. The number of recursion levels and the size of the subproblems at each level of recursion are optimized such that the problem decomposition and the solution to the problem can be obtained in constant time. As a result, they have developed some efficient merge techniques to combine the solutions for subproblems on the reconfigurable mesh. These techniques exploit reconfigurability in nontrivial ways leading to constant time solutions using optimal size of the mesh.

An optimal algorithm for the angle-restricted all nearest neighbor problem on the reconfigurable mesh, with applications

Given a set S of n points in the plane and two directions r/sub 1/ and r/sub 2/, the Angle-Restricted All Nearest Neighbor problem (ARANN, for short) asks to compute, for every point p in S, the nearest point in S lying in the planar region bounded by two rays in the directions r/sub 1/ and r/sub 2/ emanating from p. The ARANN problem generalizes the well-known ANN problem and finds applications to pattern recognition, image processing, and computational morphology. Our main contribution is to present an algorithm that solves an instance of size n of the ARANN problem in O(1) time on a reconfigurable mesh of size n/spl times/n. Our algorithm is optimal in the sense that /spl Omega/(n/sup 2/) processors are necessary to solve the ARANN problem in O(1) time. By using our ARANN algorithm, we can provide O(1) time solutions to the tasks of constructing the Geographic Neighborhood Graph and the Relative Neighborhood Graph of n points in the plane on a reconfigurable mesh of size n/spl times/n. We also show that, on a somewhat stronger reconfigurable mesh of size n/spl times/n/sup 2/, the Euclidean Minimum Spanning Tree of n points can be computed in O(1) time.

A simple Voronoi diagram algorithm for a reconfigurable mesh

In this paper, we introduce a simple and efficient algorithm for computing the Voronoi Diagram for n planar points on a reconfigurable mesh of size O(n)/spl times/O(n). The algorithm has a worst case running of O(log n log log n) time. The algorithm exploits the O(1) communication diameter of the reconfigurable mesh model to implement efficient load balancing.

CONSTANT TIME ALGORITHMS FOR GRAPH CONNECTIVITY PROBLEMS ON RECONFIGURABLE MESHES USING FEWER PROCESSORS

This paper makes an efficient improvement of processor complexity while solving some connectivity problems on a reconfigurable meshes. We first derive two constant time algorithms in the proposed parallel processing system for computing the dominators and the dominator tree of an undirected graph either using a 3-D n×n×n processors or a 2-D n2×n2 processors, where n is the number of vertices of the graph. Then based on the dominator tree algorithm, we also solve many other graph connectivity problems in a constant time. They are the articulation points, bridges, biconnected components, and bridge-connected components problem in undirected graphs.

Optimal Algorithms for Constrained Reconfigurable Meshes

This paper introduces a constrained reconfigurable mesh model which incorporates practical assumptions about propagation delays on large sized buses. Simulations ofAT2optimal reconfigurable mesh algorithms on the constrained reconfigurable mesh model are found to be nonoptimal. Optimal solutions for the sorting and convex hull problems that require less area are then presented. For the problems investigated, the constrained reconfigurable mesh model predicts a continuum in performance between the reconfigurable mesh and mesh of processors architectures.

Connected component labeling for binary images on a reconfigurable mesh architecture

Abstract We show how some existing component labeling algorithms for binary images could be speeded up by using the reconfigurable mesh architecture. Two algorithms are presented, the first one uses the ability of the reconfigurable mesh to perform certain operations in constant time, and the second one uses a bottom-up divide-and-conquer strategy. Both these algorithms have run times that are logarithmic functions of the image size.

Computing horizontal/vertical convex shape's moments on reconfigurable meshes

Zero- to third-order moments are very useful tools for analysing 2-D (two-dimensional) shapes. Given an N × N digital image, this paper presents a novel constant-time parallel algorithm for computing a horizontal/vertical convex shape's moments, each row/column in the shape without holes, on an N × N reconfigurable mesh. In the sense of the product of time and the number of processors used, our algorithm is time- and cost-optimal.

IMAGE TEMPLATE MATCHING ON RECONFIGURABLE MESHES

A mesh-connected computer enhanced by a reconfigurable bus system is referred to as a reconfigurable mesh (RM). Given an n×n grey-scale image and m×m template, in this paper, an O( log m) time parallel algorithm for template matching is presented on a RM with O(m2n2) processors. Suppose the image and template are binary, an O(1) time algorithm is presented on a RM with O(m3n2) processors. Both algorithms are superior to the best known algorithms on RMs.

Building a quadtree and its applications on a reconfigurable mesh

Quadtree is an efficient method to represent binary images. How to build a quadtree for a binary image is worthy of study. The major contribution of this paper is that we first use the Hilbert mapping technique to represent the binary image. Then, based on the reconfigurability of the reconfigurable mesh, a constant time algorithm for building a quadtree for an n × n binary image using n × n processors is derived. For applications of this algorithm two methods for compressing and decompressing binary images are also proposed.

TIME-SIZE TRADEOFFS FOR RECONFIGURABLE MESHES

Many algorithms were devised for the reconfigurable mesh model (RN-mesh) for parallel computing which involve only a constant number of broadcasting steps. It was not known, however, how tight are the constants involved. Consider an n×n directed reconfigurable mesh (DRN-mesh) that computes a function f(n) in T steps, where T is a constant. In this paper we show that T can always be reduced to a single step, still using a polynomial size DRN-mesh. Furthermore, we show that this is in fact a general tradeoff: namely, the number of steps may be reduced to any value between 1 and T, paying by an exponential growth of the size of the DRN-mesh in the number of eliminated steps.

Multiple search problem on reconfigurable meshes

In this paper, a constant time algorithm on an n 1 2 × n 1 2 × n 1 2 reconfigurable mesh is presented for solving the multiple search problem.

Constant time algorithm for computing the Hough transform on a reconfigurable mesh

A constant time algorithm is given for the reconfigurable mesh which uses an O( p log 2 N × Np) reconfigurable mesh to compute the Hough transform of N edge pixels and p angles. This algorithm is the first constant time Hough transform algorithm for a 2D reconfigurable mesh.