Minimum Broadcast Trees

Abstract

"Broadcasting" is an information dissemination process in which a member of a system generates a message communicated to all other members. We model this process by ordered rooted trees and investigate a special class of rooted trees allowing broadcasting from the root to all other vertices of the tree in the minimum time (over all rooted trees with n vertices). We characterize trees from this class ("mbt") and give an algorithm deciding membership in the class. We also present an algorithm to construct all mbt's with a given number of vertices and give a recursive formula to count these trees.