Analysis of Amnesiac Flooding
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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.
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