Optimal randomized algorithms for multipacket and cut through routing on the mesh

Presents a randomized algorithm for the multipacket (i.e. k -k) routing problem on an n×n mesh. The algorithm completes with high probability in at the most kn+O(k log n) parallel communication steps, with a constant queue size of O(k). The previous best known algorithm 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 authors also present a randomized algorithm for the cut through with partial cuts model permutation routing problem for the mesh that completes in at the most kn+ O(k log n) steps, with a constant queue size of O(k), where k is the number of flits that each packet is divided into. The previous best result was also randomized and had a time bound of kn+O(kn/ f(n)) with a queue size of O(k f (n)) (for any 1⩽f(n)⩽n). The two algorithms presented are optimal with respect to queue size. The time bounds are within a factor of two of the only known lower bound