A linear algorithm for finding the k‐broadcast center of a tree

Abstract

The term k -broadcast indicates the process of disseminating a message from one vertex to all vertices of a graph in such a way that in each time unit, an informed vertex can send the message to up to k of its neighbors. The k -broadcast center of a graph is the set of vertices that can initiate a minimum time k -broadcast within the graph. We present a linear algorithm to determine the kbroadcast center of a given tree. From this, we obtain a linear time algorithm for finding the k -broadcast time of any vertex of the tree and, thus, the k -broadcast time of the tree itself.