Global network connectivity assessment via local data exchange for underwater acoustic sensor networks

This paper studies the problem of distributed connectivity assessment for a network of underwater sensors in a data aggregation mission. Motivated by a sufficient condition for asymptotic almost sure consensus in a network defined over a random digraph, vertex connectivity of the expected communication graph is used as a measure for the connectivity of the underwater sensor network. A distributed update scheme is proposed in which the sensors update their perception of the expected communication graph. The expected communication graph can be characterized by its associated probability matrix. A learning algorithm is employed by each sensor to update its belief on the probabilities using the broadcast messages it receives. Each sensor uses a polynomial-time algorithm to estimate the degree of vertex connectivity of the expected graph based on its perception of the network graph. The proposed algorithms can also handle changes in the topology of the network such as node addition, node deletion, and time-varying probabilities. The performance of the proposed algorithms is validated in simulation.