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.

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