text: Radio networks are a long-studied model for distributed system of devices which communicate wirelessly. When these devices are mobile or have limited capabilities, the system is often best modeled by the ad-hoc variant, in which the devices do not know the structure of the network. A large body of work has been devoted to designing algorithms for the ad-hoc model, particularly for fundamental communications tasks such as broadcasting. Most of these algorithms, however, assume that devices have some network knowledge (usually bounds on the number of nodes in the network @math , and the diameter @math ), which may not always be realistic in systems with weak devices or gradual deployment. Very little is known about what can be done when this information is not available. This is the issue we address in this work, by presenting the first broadcasting algorithms for networks in which nodes have no prior knowledge whatsoever. We demonstrate that lack of parameter knowledge can be overcome at only a small increase in running time. Specifically, we show that in networks without collision detection, broadcast can be achieved in @math time, almost reaching the @math lower bound. We also give an algorithm for directed networks with collision detection, which requires only @math time.
  @cite_11: 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 - ? 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.
summary: All of these results also , and algorithms that do not require such knowledge have been little studied. The closest analogue in the literature is the work of Jurdzinski and Stachowiak @cite_11 , who give algorithms for wake-up in single-hop radio networks (those in which the underlying graph is a clique, i.e. @math ) under a wide range of node knowledge assumptions. Their Use-Factorial-Representation algorithm is the most relevant; the running time is given as @math for high-probability wake-up with a global clock (a slightly stronger task than broadcasting) in single-hop networks, but a similar analysis as we present here would demonstrate that the algorithm also performs broadcasting in multi-hop networks in @math time.