Electing a Leader in Wireless Networks Quickly Despite Jamming

In this paper we present a fast leader election protocol for single-hop wireless networks, provably robust against jamming by an external and powerful adversary. A (T,1--ε)-bounded adversary can jam at most (1--ε)w out of any w ≥ T contiguous time slots, for 0 < ε < 1. The network consists of n stations that do not have knowledge of any global parameter n, T,ε. Each station can transmit or listen to the common communication channel. In each slot, all listeners are notified in which of the three states the communication channel is in the current slot: no transmitters, exactly one transmitter or at least two transmitters. To the listening stations, a jammed slot is indistinguishable from the case of at least two transmitters. Our protocol elects a leader, with high probability, in the presence of an arbitrary, adaptive (T,1--ε)-adversary. For any constant ε and T=O{log n}, the protocol works in optimal time O{log n}. The protocol also works for general T and ε in O{log log(1/ε)/ε3 log n) slots if T ≤ log n/ε3 log(1/ε) and O{max {log log(T}/ε log n), log(1/ïε) log\log(1/ε)}T} otherwise.