Algorithms and lower bounds for p-gossiping in circulant networks

In this paper we consider the broadcast and gossiping problems in circulant networks. The circulant graphs are studied extensively as reliable interconnection networks for the multiprocessor systems. We consider gossiping in the store-and-forward, full-duplex and shouting model for the case when communicating nodes can exchange up to a fixed number p of packets at each round of gossiping (p-gossiping). A general method for evaluation of the lower bounds for p-gossiping in circulant graphs is established. The parallel decentralized node-invariant broadcast and p-gossiping algorithms are proposed which provide a minimum execution time and a minimum of message loading of a network during message-passing.