Neighbourhood information dissemination in the star graph

Abstract

This paper studies two neighborhood information dissemination problems in the star graph (n-star): The neighborhood broadcast problem (NBP) is the problem of disseminating a message from the source vertex to all the vertices adjacent to the source vertex and the neighborhood gossiping problem (NGP) is the problem of exchanging messages among all neighboring vertices in the given graph. We propose two neighborhood information dissemination schemes in n-star under the single-port, half-duplex model: The first scheme completes a neighborhood broadcast in 1.5 log/sub 2/ n+O(1) time units and the second scheme completes a neighborhood gossiping in 2.88 log/sub 2/ n+o(logn) time units. We also derive a lower bound on the neighborhood gossiping of 2.88 log/sub 2/ n+O(1) time units, which implies that the latter scheme is optimal with respect to the leading term.