An Optimal Routing Scheme for Multiple Broadcast

The dynamic broadcast problem is the communication problem where source packets to be broadcast to all the other nodes are generated at each node of a parallel computer according to a certain random process, such as a Poisson process. The lower bounds on the average reception delay required by any oblivious dynamic broadcast algorithm in a d-dimensional hypercube are Ω(d + 1 1 ρ) when packets are generated according to a Poisson process, where ρ is the load factor. The best previous algorithms for hypercubes only achieve Ω( d 1 ρ) average reception delay. In this paper, we propose dynamic broadcast algorithms that require optimal O(d+ 1 1 ρ) average reception delay in d-dimensional hypercubes and n1 n2 nd tori with ni = O(1). We apply the proposed broadcast scheme to a variety of other network topologies for efficient dynamic broadcast and present several methods for assigning priority classes to packets.