Optimal Permutation Routing on Mesh Networks

Permutation routing is used as one of the standard tests of routing algorithms. In the permutation routing problem, each processor is the origin of at most one packet and the destination of no more than one packet. The goal is to minimize the number of time steps required to route all packets to their respective destinations. Wireless mesh networks are based on plane tessellations that divide the area into cells and give rise to triangular, square, and hexagonal grids. In this paper we study permutation routing algorithms that work on finite convex subgraphs of basic grids, under the store-and-forward ∆-port model. We consider algorithms implemented independently at each node, without assuming any global knowledge about the network. I.e., distributed algorithms.