ScholarlyCommons

Title

Randomized Routing and Sorting on the Reconfigurable Mesh

Author(s)

Sanguthevar Rajasekaran, University of Pennsylvania
Theodore McKendall, University of Pennsylvania

Document Type

Technical Report

Date of this Version

May 1992

Comments

University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-92-36.

Abstract

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.

Recommended Citation

Sanguthevar Rajasekaran and Theodore McKendall, "Randomized Routing and Sorting on the Reconfigurable Mesh", . May 1992.