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On the complexity of connectivity in cognitive radio networks through spectrum assignment

Author

Listed:
  • Hongyu Liang

    (IIIS, Tsinghua University)

  • Tiancheng Lou

    (Google Inc.)

  • Haisheng Tan

    (IIIS, Tsinghua University)

  • Yuexuan Wang

    (IIIS, Tsinghua University)

  • Dongxiao Yu

    (The University of Hong Kong)

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.

Suggested Citation

  • Hongyu Liang & Tiancheng Lou & Haisheng Tan & Yuexuan Wang & Dongxiao Yu, 2015. "On the complexity of connectivity in cognitive radio networks through spectrum assignment," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 472-487, February.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:2:d:10.1007_s10878-013-9605-0
    DOI: 10.1007/s10878-013-9605-0
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    References listed on IDEAS

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    1. Shasha Li & Xueliang Li, 2012. "Note on the hardness of generalized connectivity," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 389-396, October.
    2. Hongjie Du & Weili Wu & Shan Shan & Donghyun Kim & Wonjun Lee, 2012. "Constructing weakly connected dominating set for secure clustering in distributed sensor network," Journal of Combinatorial Optimization, Springer, vol. 23(2), pages 301-307, February.
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