Abstract
Neighbor discovery is a fundamental problem in wireless networks. In this paper, we study asynchronous neighbor discovery on duty-cycled mobile devices. Most existing studies develop integer schedules where time proceeds in discrete slots and a node is awake or asleep for an entire slot duration. We show that integer schedules can lead to significant waste of resources, and develop a generalized non-integer model, where time is continuous and a node may become awake or asleep at any point of time (subject to a few constraints) so that the resultant schedules can be significantly more efficient than integer schedules. In addition, we provide a reduction that transforms any schedule in the integer model to a corresponding schedule in the generalized non-integer model while reducing the discovery latency by up to a factor of two. Applying this reduction, an optimal schedule in the integer model becomes an optimal schedule in the non-integer model. We further demonstrate the practicality of non-integer schedules in a testbed, and compare the worst-case discovery latency of several existing schemes under both integer and non-integer models. Last, we establish a family of lower bounds for the best achievable latency guarantee. These lower bounds are applicable to both integer and non-integer models, covering both symmetric and asymmetric settings, and encompassing the existing lower bounds that are only for a subset of settings as special cases.