Analysis of Amnesiac Flooding

Abstract

The purpose of the broadcast operation in distributed systems is to spread information located at some nodes to all other nodes. The broadcast operation is often realized by flooding. With flooding the source nodes send a message containing the information to all their neighbors. Each node receiving the message for the first time forwards to it all other neighbors. A stateless variant of flooding for synchronous systems is called amnesiac flooding. In this case a node after receiving a message, forwards it only to those neighbors from which it did not receive the message in the current round. In this paper we analyze the termination time of amnesiac flooding. We define the k-flooding problem. The objective is to find a set S of size k, such that amnesiac flooding when started concurrently by all nodes of S terminates in a minimal number of rounds. We provide sharp upper and lower bounds for the termination time. We prove that for every non-bipartite graph there exists a bipartite graph such that the execution of amnesiac flooding on both graphs is strongly correlated and that the termination times coincide. This construction considerably simplifies existing proofs for amnesiac flooding and gives more insight into the flooding process.

Terminating cases of flooding

“…bipartite graphs may have ec points and non-bipartite graphs may not. The recent work by Turau [40] looks at termination times in terms of the 'k-flooding problem' which aims to find a set S of size k such that amnesiac flooding when started concurrently by all nodes of S terminates in the least number of rounds.…”

“…The proof of time to termination was presented for the case of a single source, but the same proof also provides the time calculation for the multi-source case simply by replacing distances d(g 0 , g) of a node g from the initial node g 0 by distances d(I, g) of g from the set of initial nodes I. Since those publications, Turau [40,41] has worked on finding optimal sets of sources of a given size that minimize termination time for multi-source flooding. The parts of this paper from section 4 onwards on dynamic flooding, which require the use of a more powerful proof method, have not been published previously.…”