Efficient Algorithms for Neighbor Discovery in Wireless Networks

Neighbor discovery is an important first step in the initialization of a wireless ad hoc network. In this paper, we design and analyze several algorithms for neighbor discovery in wireless networks. Starting with a single-hop wireless network of n nodes, we propose a Θ(nlnn) ALOHA-like neighbor discovery algorithm when nodes cannot detect collisions, and an order-optimal Θ(n) receiver feedback-based algorithm when nodes can detect collisions. Our algorithms neither require nodes to have a priori estimates of the number of neighbors nor synchronization between nodes. Our algorithms allow nodes to begin execution at different time instants and to terminate neighbor discovery upon discovering all their neighbors. We finally show that receiver feedback can be used to achieve a Θ(n) running time, even when nodes cannot detect collisions. We then analyze neighbor discovery in a general multihop setting. We establish an upper bound of O(Δlnn) on the running time of the ALOHA-like algorithm, where Δ denotes the maximum node degree in the network and n the total number of nodes. We also establish a lower bound of Ω(Δ+lnn) on the running time of any randomized neighbor discovery algorithm. Our result thus implies that the ALOHA-like algorithm is at most a factor min(Δ,lnn) worse than optimal.