Greedy hot-potato routing on the two-dimensional mesh

Summary We propose hot-potato (or, deflection) packet routing algorithms on the two-dimensional mesh. The algorithms are strongly greedy in the sense that they attempt to send packets in good directions whenever possible. Furthermore, the routing operations are simple and independent of the time that has elapsed. The first algorithm gives the best evacuation time known for delivering all the packets to their destinations. A batch ofk packets with maximal source-to-destination distanced _max is delivered in 2(k-1)+d _max. The second algorithm improves this bound tok+d _max when all packets are destined to the same node. This also implies a new bound for the multitarget case, which is the first to take into account the number of in-edges of a node. The third algorithm is designed for routing permutations with source-to-destination distance at most three, in which case the algorithm terminates in at most seven steps. We also show a lower bound of five steps for this problem. Ishai Ben-Aroya received the B.A. and M.Sc. in computer science from the Technion (Israel Institute of Technology). He is currently working with Microsoft Israel R&D group. His main interests include Routing Algorithms, Cryptography and Computer Security. Tamar Eilam received the B.A. degree in Computer Science from the Technion IIL in 1995, and is currently studying towards her M.A. degree. Assaf Schuster received his B.A., M.A. and Ph.D. degrees in Computer Science from the Hebrew University of Jerusalem (the last one in 1991). He is currently a lecturer at the Technion IIL. His main interests include Networks and Routing Algorithms, Parallel and Distributed Computation, Optical Computation and Communication, Dynamically Reconfiguring Networks, and Greedy Hot Potato Routing.This work was supported in part by the French-Israeli grant for cooperation in Computer Science, and by a grant from the Israeli Ministry of Science. An extended abstract appeared in proc. 2nd European Symposium on Algorithms, September 1994