Probabilistic Algorithms for the Wake-Up Problem in Single-Hop Radio Networks

We consider the problem of waking up n processors in a completely broadcast system. We analyze this problem in both globally and locally synchronous models, with or without n being known to the processors and with or without labeling of the processors. The main question we answer is: how fast we can wake up all the processors with probability 1 - ε in each of these eight models? In [12] a logarithmic waking algorithm for the strongest set of assumptions is described, while for weaker models only linear and quadratic algorithms were obtained. We prove that in the weakest model (local synchronization, no knowledge of n or labeling) the best waking time is O(n/log n). We also show logarithmic or polylogarithmic probabilistic waking algorithms for all stronger models, which in some cases gives an exponential improvement over previous results.