Information Dissemination in Restricted Routing Networks

In this paper, we study a broadcast problem in directed trees. This problem is motivated by the task of implementing broadcast and multicast requests in computer systems with networks that utilize circuit routing schemes such as wormhole routing or virtual cut through routing as opposed to store and forward routing. Examples of such systems include the Intel Paragon and the NCUBE-2. The problem is deened as follows. Given a directed tree T rooted at r, we want to send a message from r to all nodes in T. We accomplish this via a broadcast schedule which consists of a number of time steps in which informed nodes deliver the message to uninformed nodes until all nodes in T have received the message. In any time step, any informed node v may forward the message to any one of its uninformed descendant nodes w via the unique directed path, or dipath, p from v to w in ditree T. We call a broadcast schedule a node disjoint broadcast schedule if the dipaths used in any time step are node disjoint. We present a dynamic programming algorithm which computes a minimum length node disjoint broadcast schedule for any directed tree T.