A Randomized Algorithm for Multipacket Routing on the Mesh

In this paper we present a randomized algorithm for the multipacket routing problem on an n×nmesh. The algorithm completes with high probability in at the most kn + o(kn) parallel communication steps, with a queue size of k + o(k). The previous best known algorithm [3] takes 5 4 kn+O( kn f(n) ) steps with a queue size of O(k f(n)) (for any 1 ≤ f(n) ≤ n). The algorithm that we will present is optimal with respect to queue size. The time bound is within a factor of two of the known lower bound.