Probabilistic Algorithms for the Wakeup Problem in Single-Hop Radio Networks

We consider the problem of waking up n processors of a completely broadcast system. We analyze this problem in both globally and locally synchronous models, with or without n being known to processors and with or without labeling of processors. The main question we answer is: how fast we can wake all the processors up with probability 1 - ? in each of these eight models. In [10] 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 poly-logarithmic waking algorithms for all stronger models, which in some cases gives an exponential improvement over previous results.

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