Routing and sorting on meshes with row and column buses

We give improved deterministic algorithms for permutation routing and sorting on meshes with row and column buses. Among our results, we obtain a fairly simple algorithm for permutation routing on two-dimensional meshes with buses that achieves a running time of n + o(n) and a queue size of 2. We also describe an algorithm for routing on r-dimensional networks with a running time of (2-1/ r)n+o(n) and a queue size of 2, and show how to obtain deterministic algorithms for sorting whose running times match those for permutation routing. An interesting feature of our algorithms is that they can be implemented on a wide variety of different models of meshes with buses within the same bounds on time and queue size. finally, we also study the performance of meshes with buses on dynamic routing problems, and propose fast routing schemes under several different assumptions about the properties of the bus system.