Madhusudan Nigam

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.

Sorting n numbers on n × n reconfigurable meshes with buses

Abstract We show how column sort and rotate sort can be implemented on the different reconfigurable mesh with buses (RMB) architectures that have been proposed in the literature. On all of these proposed RMB architectures, we are able to sort n numbers on an n × n configuration in O (1) time. For the PARBUS RMB architecture, our column sort and rotate sort implementations are simpler than the O (1) sorting algorithms developed in Jang and Prasanna ( International Parallel Processing Symposium , 1992) and Lin et al . ( Proceedings of Ninth European Workshop on Parallel Computing , 1992). Furthermore, our sorting algorithms use fewer bus broadcasts. For the RMESH RMB architecture, our algorithms are the first to sort n numbers on an n × n configuration in O (1) time. We also observe that rotate sort can be implemented on N × N × ··· × N ( k + 1)-dimensional RMB architectures to sort N k elements in O (1) time.

Sorting n/sup 2/ numbers on n*n meshes

The authors show that by folding data from an n*n mesh onto an n*(n/k) submesh, sorting on the submesh, and finally unfolding back onto the entire n*n mesh it is possible to sort on bidirectional and strict unidirectional meshes using a number of routing steps that is very close to the distance lower bound for these architectures. The technique may also be applied to reconfigurable bus architectures to obtain faster sorting algorithms.<<ETX>>

Triangulation on a Reconfigurable Mesh with Buses

We develop an 0(1) time algorithm to a triangulate a set of N planar points using an N¿N reconfigurable mesh with buses. Our algorithm works on all reconfigurable mesh with buses architectures.

Sorting n/sup 2/ numbers on n/spl times/n meshes

We show that by folding data from an n/spl times/n mesh onto an n/spl times/(n/k) submesh, sorting on the submesh, and finally unfolding back onto the entire n/spl times/n mesh it is possible to sort on bidirectional and strict unidirectional meshes using a number of routing steps that is very close to the distance lower bound for these architectures.We show that by folding data from an n×n mesh onto an n× (n/k) submesh, sorting on the submesh, and finally unfolding back onto the entire n×n mesh it is possible to sort on bidirectional and strict unidirectional meshes using a number of routing steps that is very close to the distance lower bound for these architectures.

Parallel programming on reconfigurable meshes with buses

Several mesh-like architectures have been proposed to support parallel computing. These connect the processor mesh with a system of reconfigurable buses. In this work, the authors present several examples to illustrate the ease with which efficient (in fact, constant time) programs can be developed for the weakest of these architectures. The examples are from computational geometry.<<ETX>>