Parallel Routing and Sorting of the Pancake Network

The pancake graph along with the star graph were proposed in 1986 [1] as attractive alternatives to the hypercube topology for interconnecting processors in a parallel computer. In this paper, we study some of their topological properties. We then present parallelrouting schemes for both networks. Finally, we present an efficient algorithm for sorting K numbers on a pancake interconnection network with n! nodes, where K≥n!, and each node holds at most N=[K/n!] numbers;the algorithm runs in O(NlogN(nlogn)+Nn3logn) time, which is O(n3logn) when K=n!.