Optimal all-to-all broadcasting schemes in distributed systems

Broadcasting, which refers to a process of information dissemination in a distributed system whereby a message originating from a certain node is sent to all other nodes in the system, is a very important issue in distributed computing. All-to-all broadcasting means the process by which every node broadcasts its certain piece of information to all other nodes. The authors develop optimal all-to-all broadcasting schemes for a distributed system of an arbitrary number of nodes to complete the broadcasting with not only the minimal number of communication steps but also the minimal number of messages. They develop the optimal all-to-all broadcasting scheme for the case of k-port communication, meaning that each node can send out k messages in one communication step where k is a positive integer depending on the system. It is shown that the proposed scheme not only requires the minimal number of communication steps but also incurs the minimal number of messages