Randomized Leader Election Protocols Ad-hoc Networks K. NAKANO Nagoya Institute of Technology, Japan S. OLARIU Old Dominion University, U.S.A. Abstract Unlike the well-studied cellular networks that assume the existence o robust infrastructure, Ad-hoc Networks (AHN, for short) are rapidly deplo able, self-organizing, and do not rely on an existing infrastructure. These ne works find applications to disaster-relief, search-and-rescue, law-enforcem and collaborative computing, among others. The main contribution of this work is to propose an extremely fast lead election protocol for AHNs. We begin by showing that for every f 1 single-hop single-channel n-station AHN can elect a leader among n ide tical stations in loglog n 2 78log f o log log n log f time slots w probability at least 1 1 f . Second, we show an important application of our protocol to collisi resolution in single-hop, k-channel AHNs. More specifically, once we an arbitrary f 1, the collision resolution problem in such a model can solved in loglog n 2 78log k 2 78log f o log log n log k log f tim slots with probability at least 1 1 f . Finally, we address the leader election problem on the single-chann AHN with diameter two. In this latter case we exhibit a leader election pr tocol terminating, with probability at least 1 1 f , in 2 log log n 11 10log f o log log n log f time slots, for every f 1. Keywords Ad-hoc Networks, leader election, randomized algorithms. 1 Introduction An Ad-hoc Network (AHN, for short) is a distributed system with no ce biter, consisting of n radio transceivers, henceforth referred to as stations. tions communicate using k communication channels denoted by C 1 C2 Work supported, in part, by the NSF grant CCR-9522093 and by ONR grant N00014-9 1