Tree bound on probabilistic connectivity of Underwater Sensor Networks

This paper considers Underwater Sensor Networks (UWSNs) with unanchored nodes that can move freely with water currents. Thus, node locations at any instant can only be specified probabilistically. When connectivity among some of the sensor nodes is required to perform a given function, the problem of estimating the likelihood that the network achieves such connectivity arises. Our work here formulates a parameterized probabilistic connectivity problem that serves this purpose when the network contains both sensor nodes and relay nodes. We show an exact dynamic programming algorithm for solving the problem on networks with tree-like structure; the algorithm yields lower bounds on the solution of the problem on any arbitrary network. The obtained simulation results investigate the gap between our obtained lower bounds and exact solutions on small networks, as well as the usefulness of our method in analyzing the effect of adding relay nodes to the network.