An Improved Approximation Algorithm for the Shortest Link Scheduling Problem 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 SINR and hypergraph models, and propose an approximation algorithm GeoSLS by using geometric links for better performance than GOW* proposed by Blough, Resta and Santi(2010). For the average length of scheduling, GeoSLS decreases 1/m compared with GOW*, where $m=\lfloor 4p+(\Delta_{max}-4)\cdot (1-p)\rfloor$ is the expected number of the links in the set V returned by HyperMaxLS and 0 < p < 1 is the probability of the number of the links scheduled simultaneously in the set V. In the worst, ideal and average cases, the ratios of time complexity of our algorithm GeoSLS to GOW* are $O(\Delta_{max}/\overline{k})$, $O(1/(\overline{k}\cdot\Delta_{max}))$ and $O(\Delta_{max}/(\overline{k}\cdot m))$, respectively, where $1<\overline{k}<\Delta_{max}$ is a constant called the SNR diversity of instance G.

The work is supported by NNSF of China for contract(61373027, 11101243) and NSF of Shandong Province for contract(ZR2012FM023).