Multi-Node Broadcasting in Hypercubes and Star Graphs

Technological advances have made building complicated large-scale multicomputer networks possible. The binary hypercube [7] is undoubtedly one of the most popular interconnection networks for parallel processing. Another candidate is the star graph [1], which has been recognized as an attractive alternative to the hypercube. A large number of researches have studied the star graph, focusing on its topological properties [3, 11], embedding capability [6, 13], and communication capability [2, 8, 10, 14]. Given an interconnection network, one important issue is how to perform broadcasting, such as one-to-all broadcasting and all-to-all broadcasting. In this paper, we take one further step and study the multi-node broadcasting (or manyto-all broadcasting) problem in hypercubes and star graphs, where there is an arbitrary set of nodes in the network, each intending to broadcast a message to the rest of the network. This generalizes the one-to-all and all-to-all broadcasting problems. These broadcasting operations fall within the realm of collective communication in interconnection networks and can be found in many applications, such as parallel graph algorithms, parallel matrix algorithms, fast Fourier transformation, parallel compilers, cache coherence, etc. In the multi-node broadcasting problem under consideration here, it is not known in advance how many nodes intend to perform the broadcast operation.