 
Summary: Efficient line broadcasting in trees
A. Averbuch \Lambda
I. Gaber y
Y. Roditty z
Abstract
Efficient algorithms for line broadcasting in Complete Binary and Binomial trees,
are presented. They have linear in n(the number of vertices), complexity. This answers
a question raised by Fujita and Farley [5]. An insight on some other trees is given, as
well.
1 Introduction
Let G = G(V; E) be a connected graph. A communication network is defined as a connected
graph. Given a set A ae V (G); A 6= Ø, we define broadcasting (multicasting) from A to be
the process of transmitting one (many) unit(s) of information from A to all the vertices in
G n A ( B ae (G n A) ). The vertices in A are called originators. This is accomplished by
a series of transitions over G. The messages are distributed over G and spread through the
edges, where each vertex transmits a message to its neighbors upon receiving it regardless
of the activities in other vertices (besides the vertex that receives the message that has to
be idle). This procedure is called local.
In line broadcasting an informed vertex may call any other vertex using the communi
cation links of any simple path between the two vertices with the restriction that no link
