The complexity of channel scheduling in multi-radio multi-channel wireless networks

The complexity of channel scheduling in Multi-Radio Multi-Channel (MR-MC) wireless networks is an open research topic. This problem asks for the set of edges that can support maximum amount of simultaneous traffic over orthogonal channels under a certain interference model. There exist two major interference models for channel scheduling, with one under the physical distance constraint, and one under the hop distance constraint. The complexity of channel scheduling under these two interference models serves as the foundation for many problems related to network throughput maximization. However, channel scheduling was proved to be NP-Hard only under the hop distance constraint for SR-SC wireless networks. In this paper, we fill the void by proving that channel scheduling is NP-Hard under both models in MR-MC wireless networks. In addition, we propose a polynomial-time approximation scheme (PTAS) framework that is applicable to channel scheduling under both interference models in MR-MC wireless networks. Furthermore, we conduct a comparison study on the two interference models and identify conditions under which these two models are equivalent for channel scheduling.