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

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 S L S p c (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 S L S p c is 1 / m of GOW*, where m = ⌊ Δ m a x · p ⌋ 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 S L S p c to that of GOW* are O ( Δ m a x / k ¯ ) , O ( 1 / ( k ¯ · Δ m a x ) ) and O ( Δ m a x / ( k ¯ · m ) ) , respectively. Where k ¯ ( 1 < k ¯ < Δ m a x ) is a constant called the SNR diversity of an instance G .