New Construction of Broardcast Graphs

Abstract

Broadcast algorithms are are very important in parallel and distributed computing. In this paper we design new sparce graphs and present a minimum time broadcast algorithms from any vertex of these graphs. A broadcast graph on n vertices is a graph which allows any vertex to broadcast in time [log n]. A minimum broadcast graph on n vertices is a broadcast graph with the minimum number of edges over all broadcast graphs on n vertices. This minimum number of edges is denoted by B(n). Many papers have presented methods to construct broadcast graphs. Here we present a method to construct a broadcast graph on n + 1 vertices by adding a vertex to a broadcast graph on n vertices. Our general upper bound on B(n) improves the best known upper bounds for almost all odd values of n. Our broadcast algorithms are simple. Our new broadcast graphs can be combined using some of the known methods to obtain further improvements.