Randomized 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 (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

Permutation routing and sorting on the reconfigurable mesh

Abstract In this paper we demonstrate the power of reconfiguration by pre-senting 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. Wealsomakeuseofthestandard PARBUS model. We showthat permutation routing problem can be solved on a linear array Mr of size n in 3n steps, whereas n − 1 is the best possible run time without recon-4 figuration. A trivial lower bound for routing on Mr will be n 2.OnthePARBUS linear array, n is a lower bound and hence any standard n-step routing algorithm will be optimal. We also showthat 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 1 hand, n is a lower bound for routing on the PARBUS and our algorithms have the same time bounds on the PARBUS as well. Thus our randomized routing algorithm is optimal upto a lower order term. In addition we show that the problem of sorting can be solved in randomized time n + o(n) onMr as well as on PARBUS. Clearly, this sorting algorithm will be optimal on the PARBUS model. The time bounds of our randomized algorithms hold with high probability