An optimal algorithm for broadcasting multiple messages in trees

We consider multiple message broadcasting in tree networks. The source (considered as the root of the tree) has k messages which have to be broadcast to all nodes of the tree. In every time unit each node can send one of its already obtained messages to one of its children. A ii-message broadcasting scheme prescribes in which time unit a given node should send a message to which child. It is k-optimal if it achieves the smallest possible time for broadcasting k messages from the source to all nodes. We give an algorithm to construct a k-optimal broadcasting scheme for an arbitrary n-node tree. The time complexity of our algorithm is O(nk), i.e., the best possible, (C) 1999 Academic Press.