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We consider a topology control problem in which we are given a set of sensors in RdRd and we would like to assign a communication radius to each of them so that they generate a connected network and have low receiver-based interference (defined as the largest in-degree of the network). We show that any radii assignment that generates a connected network can be modified so that interference is (asymptotically) unaffected and no sensor is assigned communication radius larger than RminRmin, where RminRmin is the smallest possible radius needed to obtain strong connectivity. Combining this result with the previous network construction methods (see Halldórsson and Tokuyama (2008)  and von Rickenbach et al. (2009) ), we obtain a way to construct a connected network of low interference and bounded radii. Since the radius of a sensor is only affected by neighboring sensors, this construction can be done in a distributed fashion.
CitationKorman, M. Minimizing interference in ad hoc networks with bounded communication radius. "Information processing letters", 15 Octubre 2012, vol. 112, núm. 19, p. 748-752.
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