Broadcasting in general networks I: Trees

Abstract

Broadcasting is the process of information dissemination in communication networks whereby a message originated at one vertex becomes known to all members given that at each unit of time a vertex can pass the message to at most one of its neighbours. In this paper we consider the problem of broadcasting in trees which is a step towards studying broadcasting in general graphs, as oppose to the much studied problem of constructing broadcast graphs having the smallest number of edges in which message can be broadcast in minimum possible (= [log₂ n]) steps regardless of originator. Trees with the smallest possible broadcast time are exhibited for all n≤326, and for n sufficiently large existence of trees with broadcast time roughly 3/2 log₂ n is shown. It is also shown that broadcast time of a general tree can be computed in O(n) time.

Part of this work was done while the author was visiting Department D'Informatique, Université Du Maine, Le Mans, France under Marie-Curie Fellowship of CEC (contract No. CI1^*-CT-93-0234). Research also supported in part by the Department of Science and Technology, Govt. of India grant no. SR/OY/E-06/93.