Abstract
Cognitive Radio Networks (CRNs) are considered as a promising solution to the spectrum shortage problem in wireless communication. In this paper, we initiate the first systematic study on the algorithmic complexity of the connectivity problem in CRNs through spectrum assignments. We model the network of secondary users (SUs) as a potential graph, where two nodes having an edge between them are connected as long as they choose a common available channel. In the general case, where the potential graph is arbitrary and the SUs may have different number of antennae, we prove that it is NP-complete to determine whether the network is connectable even if there are only two channels. For the special case where the number of channels is constant and all the SUs have the same number of antennae, which is more than one but less than the number of channels, the problem is also NP-complete. For the special cases in which the potential graph is complete, a tree, or a graph with bounded treewidth, we prove the problem is NP-complete and fixed-parameter tractable when parameterized by the number of channels. Exact algorithms are also derived to determine the connectability of a given cognitive radio network.
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Notes
We assume two heterogenous SUs cannot communicate even when they work on a common channel and their distance is within their transmission ranges.
This can be seen as a generalization of the connectivity concept in graphs. There are also many other types of generalizations, such as the generalized connectivity studied in Li and Li (2012).
Commonly, the white spaces include spectrums from channel 21 (512 Mhz) to 51 (698 Mhz) excluding channel 37, which is totally 29 channels Bahl et al. (2009).
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Acknowledgments
The authors would like to give thanks to Dr. Thomas Moscibroda at Microsoft Research Asia for his introduction of the original problem. This work was supported in part by the National Basic Research Program of China Grant 2011CBA00300, 2011CBA00302, the National Natural Science Foundation of China Grant 61073174, 61103186, 61202360, 61033001, and 61061130540.
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A preliminary version of this paper appeared in ALGOSENSORS 2012 Liang et al. (2013). The main extensions are that we give more details of our results and investigate the special case where the potential graphs are of bounded treewidth.
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Liang, H., Lou, T., Tan, H. et al. On the complexity of connectivity in cognitive radio networks through spectrum assignment. J Comb Optim 29, 472–487 (2015). https://doi.org/10.1007/s10878-013-9605-0
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DOI: https://doi.org/10.1007/s10878-013-9605-0