Weak communication in single-hop radio networks: adjusting algorithms to industrial standards

Quite often algorithms designed for no-collision-detection radio networks use a hidden form of collision detection: it is assumed that a station can simultaneously send and listen. If it cannot hear its own message, apparently the message has been scrambled by another station sending at the same time. Industrial standard IEEE 802.11 says that a station can either send or listen to a radio channel at a given time, but not both. In order to relate the industrial standard and theoretical algorithms we consider a weak radio network model with no collision detection in which a station cannot simultaneously send and receive signals. Otherwise we talk about a strong model. In this paper we consider a measure called energy cost (or 'power consumption') which is equal to the maximum over all stations of the number of steps in which the station is sending or listening. We show that computational power of weak and strong single-hop radio networks differ substantially in the deterministic case: deterministic leader election requires Omega (rootlog n) energy cost in the weak model and can be solved by a practical algorithm with O(rootlog n) energy cost in the strong model. By contrast, we present a very efficient randomized simulation of strong radio networks by weak ones, with preprocessing that requires O(n) steps and has energy cost O(log log n). Copyright (C) 2003 John Wiley Sons, Ltd.