### An Energy-Optimal Algorithm for Neighbor Discovery in Wireless Sensor Networks

- R. Madan and S. Lall.
- Proceedings of Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt), p. 272--281, 2004.

We consider sensor networks in which individual nodes with on-board sensing and low-power transmitters and receivers establish connections with neighboring nodes. The overall objective is to enable energy-efficient data communication, relayed between arbitrary nodes on the network. We develop a distributed algorithm which minimizes the energy required for neighbor discovery. Initially nodes do not have deterministic knowledge of the location of their neighbors, and we model the distribution of the nodes as a two-dimensional Poisson process with known intensity. This corresponds to a situation in which a large number of nodes are randomly distributed over a given area. The process of neighbor discovery is modeled as a Markov decision process, and the resulting control policy is a finite automaton, driven by the underlying probability distribution, that minimizes the average energy consumed. This policy can be computed offline and stored in each node with very low requirements for online memory and processor capability.