Broadcasting from multiple originators

We begin an investigation of broadcasting from multiple originators, a variant of broadcasting in which any k vertices may be the originators of a message in a network of n vertices. The requirement is that the message be distributed to all n vertices in minimum time. A minimum k-originator broadcast graph is a graph on n vertices with the fewest edges such that any subset of k vertices can broadcast in minimum time. Bk(n) is the number of edges in such a graph. In this paper, we present asymptotic upper and lower bounds on Bk(n). We also present an exact result for the case when k ≥ 2 . We also give an upper bound on the number of edges in a relaxed version of this problem in which one additional time unit is allowed for the broadcast. keywords: broadcast, multiple originator, minimum broadcast graph, relaxed broadcast Preprint submitted to Elsevier 10 February 2009