Mesh Connected Computers with Fixed and Reconfigurable Buses: Packet Routing, Sorting, and Selection

Mesh connected computers have become attractive models of computing because of their varied special features. In this paper we consider two variations of the mesh model: 1) a mesh with fixed buses, and 2) a mesh with reconfigurable buses. Both these models have been the subject matter of extensive previous research. We solve numerous important problems related to packet routing, sorting, and selection on these models. In particular, we provide lower bounds and very nearly matching upper bounds for the following problems on both these models: 1) Routing on a linear array; and 2) k − k routing, k − k sorting, and cut through routing on a 2D mesh for any k ≥ 12. In addition we present greedy algorithms for 1 − 1 routing, k − k routing, cut through routing, and k − k sorting that are better on average and supply matching lower bounds. We also show that sorting can be performed in logarithmic time on a mesh with fixed buses. As a consequence we present an optimal randomized selection algorithm. Further, we provide a selection algorithm for the mesh with reconfigurable buses whose time bound is significantly better than the existing ones. Most of our algorithms have considerably better time bounds than known algorithms for the same problems.