Broadcasting from multiple originators

Authors:
Arthur L. Liestman;Dana Richards;Ladislav Stacho
Affiliations:
School of Computing Science, Simon Fraser University, Burnaby, BC V5A 1S6, Canada;Department of Computer Science, George Mason University, MSN 4A5, 4400 University Drive, Fairfax, VA 22030, USA;Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

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 minimumk-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. B"k(n) is the number of edges in such a graph. In this paper, we present asymptotic upper and lower bounds on B"k(n). We also present an exact result for the case when k=n2. 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.