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 /spl Omega/(d+1/1-/spl rho/) when packets are generated according to a Poisson process, where p is the load factor. The best previous algorithms for hypercubes only achieve /spl Omega/(d/1-/spl rho/) average reception delay. In this paper, we propose dynamic broadcast algorithms that require optimal O(d+1/1-/spl rho/) average reception delay in d-dimensional hypercubes and n/sub 1//spl times/n/sub 2//spl times//spl middot//spl middot//spl middot/n/sub d/ tori with n/sub i/=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.