Abstract
Neighbor discovery is a fundamental problem in wireless networks. In this paper, we study asynchronous neighbor discovery between duty-cycled mobile devices. Each node is duty-cycled, i.e., its radio may only be active for a small fraction of the time. The duty cycles of the nodes can be the same or different, leading to symmetric or asymmetric cases of the neighbor discovery problem. In addition, the setting is asynchronous, i.e., clocks of different nodes may not be synchronized. Most existing studies assume an integer model (where time proceeds in discrete steps); two recent studies break away from this assumption, which allows them to develop significantly more efficient schemes. Our study improves the state-of-the-art in three main fronts. Firstly, we develop a generalized non-integer model (where time is continuous) that permits unified treatment of the assumptions in existing studies. We also provide a reduction that transforms any schedule in the basic integer model to a corresponding schedule in the generalized non-integer model while improving the performance by a factor of two. Applying this reduction, an optimal schedule in the integer model becomes an optimal schedule in the non-integer model. Thirdly, we establish a new family of lower bounds for the best achievable latency guarantee in the non-integer model. They are applicable to both symmetric and asymmetric settings, and encompass the lower bounds for the integer model as special cases. Finally, we develop a novel optimal construction based on Sidon sets for the symmetric setting. Our approach differs from the approaches taken by all existing studies, and provides a new direction for constructing neighbor discovery schedules.