Line broadcasting in cycles Original Research Article

Broadcasting is the process of transmitting information from an originating node (processor) in a network to all other nodes in the network. A local broadcast scheme only allows a node to send information along single communication links to adjacent nodes, while a line broadcast scheme allows nodes to use paths of several communication links to call distant nodes. The minimum time possible for broadcasting in a network of n nodes when no node is involved in more than one communication at any given time is ⌊ log n⌋ phases. Local broadcasting is not sufficient, in general, for broadcasting to be completed in minimum time; line broadcasting is always sufficient. An optimal line broadcast is a minimum-time broadcast that uses the smallest possible total number of communication links. In this paper, we give a complete characterization of optimal line broadcasting in cycles, and we develop efficient methods for constructing optimal line broadcast schemes.