Greedy Hot-Potato Routing on the Mesh

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. These two features suggest that the algorithms are practical and may also be used for continuous routing. The first algorithm gives the best evacuation time known for delivering all the packets to their destinations. A batch of k packets with maximal source-to-destination distance d max is delivered in 2(k −1)+d max . The second algorithm improves this bound to k+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 in which the maximal source-to-destination distance is small. In particular, when routing permutations for which d max =3, the algorithm terminates in at most seven steps. We also show a lower bound of five steps for this problem.