Optimal Randomized Algorithms for Multipacket and Wormhole Routing on the Mesh

In this paper, we present a randomized algorithm for the multipacket (i.e., k k) routing problem on an n x n mesh. The algorithm competes with high probability in at most kn + O(k log n) parallel communication steps, with a constant queue size of O(k). The previous best known algorithm [4] takes [5/4] kn + O([kn/f(n)]) steps with a queue size of O(k f(n)) (for any 1 ≤ f (n) ≤ n). We will also present a randomized algorithm for the wormhole 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 [6] 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). The two algorithms that we will present are optimal with respect to queue size. The time bounds are within a factor of two of the only known lower bound. Comments University of Pennsylvania Department of Computer and Information Sciences Technical Report No. MSCIS-91-47. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/329 Optimal Randomized Algorithms For Multipacket And Wormhole Routing On The Mesh MS-CIS-91-47 GRASP LAB 269 Sangut hevar Rajasekaran Mukund Raghavachari Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 19104-6389