The priority broadcast scheme for dynamic broadcast in hypercubes and related networks

Dynamic broadcast is a communication problem where each node in a parallel computer generates packets to be broadcast to all the other nodes according to a certain random process. The lower bound on the average time required by any oblivious dynamic broadcast algorithm in an n-dimensional hypercube is Ω(n+1/(1-ρ)) when packets are generated according to a Poisson process, where ρ is the load factor. The best previous algorithms, however only achieve Ω(n/(1-ρ)) time, which is suboptimal by a factor of Θ(n). In this paper we propose the priority broadcast scheme for designing dynamic broadcast algorithms that require optimal O(n+1/(1-ρ)) time in an n-dimensional hypercube. We apply the routing scheme to other network topologies, including k-ary n-cubes, meshes, tori, star graphs, generalized hypercubes, as well as any symmetric network, for efficient dynamic broadcast. In particular the algorithms for star graphs, generalized hypercubes, and k-ary n-cubes with k=0(1) are also asymptotically optimal. We also propose a method for assigning priority classes to packets, called optimal priority assignment, which achieves the best possible performance for dynamic multiple broadcast in any network topology