Permutation 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. The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. Many variations of the reconfigurable mesh can be found in the literature. We define yet another variation which we call as Mr. We also make use of the standard PARBUS model. We show that permutation routing problem can be solved on a linear array Mr of size n in 3 4 n steps, whereas n− 1 is the best possible run time without reconfiguration. A trivial lower bound for routing on Mr will be n 2 . On the PARBUS linear array, n is a lower bound and hence any standard n-step routing algorithm will be optimal. We also show that permutation routing on an n× n reconfigurable mesh Mr 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. A lower bound of n 2 is in effect for routing on the 2D mesh Mr as well. On the other