Analysis of Spectral Properties for Efficient Coverage Under Probabilistic Flooding

Abstract

Information dissemination plays a crucial role in modern network environments being an integral part of various vital processes (e.g., service discovery, data collection, routing). Probabilistic flooding has been proposed as a suitable alternative to blind flooding in order to reduce unnecessary transmissions and save valuable network resources. Under probabilistic flooding, an information message, initially located at some network node (i.e., the initiator node), is transmitted to neighbor nodes according to a forwarding probability attempting to reach all network nodes. This paper employs elements from algebraic graph theory to model probabilistic flooding behavior and derive analytical results regarding coverage (i.e., the number of nodes that have received the information message) and a lower bound of the forwarding probability allowing for global network outreach. It is also shown here, that for any value of the forwarding probability larger than this lower bound, (i) coverage under probabilistic flooding, is proportional to the initiator's node eigenvector centrality; and (ii) the probability for a node to receive the information message is proportional to the particular node's eigenvector centrality. Simulations performed for various topologies demonstrate the effectiveness of the proposed analytical model and support the analytical results.