Probabilistic flooding in stochastic networks: Analysis of global information outreach

This article investigates probabilistic information dissemination in stochastic networks. The following problem is studied: A source node intends to deliver a message to all other network nodes using probabilistic flooding, i.e., each node forwards a received message to all its neighbors with a common network-wide forwarding probability ω. Question is: what is the minimum ω-value each node should use, such that the flooded message is obtained by all nodes with high probability? We first present a generic approach to derive the global outreach probability in arbitrary networks and then focus on Erdős Rényi graphs (ERGs) and random geometric graphs (RGGs). For ERGs we derive an exact expression. For RGGs we derive an asymptotic expression that represents an approximation for networks with high node density. Both reliable and unreliable links are studied.