Neighbor discovery in wireless networks and the coupon collector's problem

—Neighbor discovery1 is one of the first steps in the initialization of a wireless ad hoc network. In this paper, we design and analyze practical algorithms for neighbor discovery in wireless networks. We first consider an ALOHA-like neighbor discovery algorithm in a synchronous system, proposed in an earlier work. When nodes do not have a collision detection mechanism, we show that this algorithm reduces to the classical Coupon Collector’s Problem. Consequently, we show that each node discovers all its n neighbors in an expected time equal to ne(ln n + c), for some constant c. When nodes have a collision detection mechanism, we propose an algorithm based on receiver status feedback which yields a ln n improvement over the ALOHA-like algorithm. Our algorithms do not require nodes to have any estimate of the number of neighbors. In particular, we show that not knowing n results in no more than a factor of two slowdown in the algorithm performance. In the absence of node synchroniz...

• Type: Conference
• Year: 2009
• Where: MOBICOM
• Authors: Sudarshan Vasudevan, Donald F. Towsley, Dennis Goeckel, Ramin Khalili
• Keywords: Algorithms, Communications, MOBICOM 2009, Neighbor Discovery, Neighbor Discovery Algorithms