Annual Conference of ITA ACITA 2009

1. One-and-only-one transmit: That ID is discovered (by all) Idle: No discovery Collision: No discovery Annual Conference of ITA ACITA 2009 Neighbor Discovery in Wireless Networks and the Coupon Collector’s Problem Sudarshan Vasudevan (UMass), Don Towsley (UMass), Dennis Goeckel (UMass) and Ramin Khalili (EPFL)* • What is missing? • No apriori transmission scheduling among nodes can cause interference • No prior knowledge of node density • Lack of synchronization among nodes • Detecting when to start and terminate neighbor discovery phase non-trivial • Problem Definition • Nodes have just been placed/thrown/dropped • Every node has a unique ID • Nodes are beginning to power up • How does each node determine the IDs of its neighbors to begin ad hoc network formation? • Challenge: Nothing is knownat the time of deployment • Prior Work • Aloha-like ND Algorithms [MMcGlynn01,SVasudevan05,SBorbash07] • Focus on determining optimal p • Time required to discover all neighbors under optimal settings unknown • Assume prior information about node density • ND initiation/termination not handled • Typical Approach • ALOHA – each node transmits with probability p • Removing Assumptions • Unknown n: Algorithm execution in phases • In phase j, transmit with probability • Only a factor 2 slowdown from knowing n • Asynchronism: Collision duration doubled • Each phase 2 times longer • Factor of 2 slowdown from synchronous execution • Account for clock skews to allow different start times • Termination condition based on number of nodes discovered in each phase • Aloha-like Discovery • Assume node density known and perfect synchronization among nodes • Nodes cannot distinguish between collision and idle time slot (hence, a node does not know when it has been discovered) • Each node transmits with p = 1/n • Our Key Observation: Reduces to Coupon Collector’s Problem • Time to discover all neighbors • Conclusions • Result: a ND algorithm running in time when there is no feedback and time when nodes provide feedback of reception status, with no assumptions on: • Knowledge of number of neighbors • Synchronization among nodes • Initial starting time • Knowledge of when to terminate • Collision Detection-based ND • Each node sends feedback of reception status • Once a node has been discovered by its neighbors, it stops transmitting • A factor of ln n improvement in time to discover neighbors, which is • Order optimal • Unknown node density, asynchronous execution and initiation/termination • Handled similar to Aloha-like neighbor discovery * Portion of work done when the author was a post-doctoral researcher at UMass Amherst