A decentralised scheme for multi-node broadcasting on hypercubes

In this paper, we study the following multi-node broadcast problem on hypercubes, which is an asynchronous and repetitive version of all-to-all broadcast problem. Suppose that nodes of a hypercube asynchronously repeat broadcasting a piece of information called a token. They can asynchronously initiate their broadcasts while other broadcasts are in process. The multi-node broadcast problem, which we discuss in this paper, is the problem of completing each of these broadcasts quickly. It is neither the broadcast problem, which assumes that no nodes initiate a broadcast while a broadcast is in process, nor the gossip problem, which assumes that all nodes initiate broadcasts simultaneously. We propose an adaptive scheme SORT for solving the problem in such a way that each initiator of a broadcast determines the broadcast route based only on local information. The effectiveness of SORT is demonstrated by simulations