A Lower Bound for Oblivious Dimensional Routing

Abstract

In this work we consider deterministic oblivious dimensional routing algorithms on d-dimensional meshes. In oblivious dimensional routing algorithms the path of a packet depends only on the source and destination node of the packet. Furthermore packets use a shortest path with a minimal number of bends. We present an Ω(kn (d+1)/2 ) step lower bound for oblivious dimensional k-k routing algorithms on d-dimensional meshes for odd d > 1 and show that the bound is tight.