Doubly-logarithmic energy-efficient initialization protocols for single-hop radio networks

A radio network is a distributed system with no central shared resource, consisting of n stations each equipped with a radio transceiver. One of the most important parameters to evaluate protocols in the radio networks is the number of awake time slots in which each individual station sends/receives a data packet. We are interested in devising energy-efficient initialization protocols in the single-hop radio network (RN, for short) that assign unique IDs in the range [1, n] to the n stations using few awake time slots. It is known that the RN can be initialized in O(log log n) awake time slots, with high probability, if every station knows the number n of stations in the RN. Also, it has been shown that the RN can be initialized in O(log n) awake time slots even if no station knows n. However, it has been open whether the initialization can be performed in O(log log n) awake time slots when no station knows n.Our main contribution is to provide the breakthrough: we show that even if no station knows n, the RN can be initialized by our protocol that terminates, with high probability, in O(n) time slots with no station being awake for more than O(log log n) time slots. We then go on to design an initialization protocol for the k-channel RN that terminates, with high probability, in O(n/k+(log n)2) time slots with no station being awake for more than O(log log n) time slots.