An improved approximation algorithm for the shortest link scheduling in wireless networks under SINR and hypergraph models

Abstract

Link scheduling is a fundamental problem in wireless ad hoc and sensor networks. In this paper, we focus on the shortest link scheduling (SLS) under Signal-to-Interference-plus-Noise-Ratio and hypergraph models, and propose an approximation algorithm $SLS_{pc}$ (A link scheduling algorithm with oblivious power assignment for the shortest link scheduling) with oblivious power assignment for better performance than GOW* proposed by Blough et al. [IEEE/ACM Trans Netw 18(6):1701–1712, 2010]. For the average scheduling length of $SLS_{pc}$ is 1 / m of GOW*, where $m=\lfloor \varDelta _{max}\cdot p \rfloor$ is the expected number of the links in the set V returned by the algorithm HyperMaxLS (Maximal links schedule under hypergraph model) and $0<p<1$ is the constant. In the worst, ideal and average cases, the ratios of time complexity of our algorithm $SLS_{pc}$ to that of GOW* are $O(\varDelta _{max}/\overline{k})$, $O(1/(\overline{k}\cdot \varDelta _{max}))$ and $O(\varDelta _{max}/(\overline{k}\cdot m))$, respectively. Where $\overline{k}$ ($1<\overline{k}<\varDelta _{max}$) is a constant called the SNR diversity of an instance G.