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Shortest link scheduling (SLS) in multihop wireless networks under physical interference model is notoriously hard to resolve and been studied only recently by a few works. Most of the obtained approximation bounds grow linearly with the number of links, and many are only valid with single-hop wireless networks, and some claimed approximation bounds are even false. This paper conducts a rigorous algorithmic study of SLS with power control under the physical interference model. We develop a polynomial O (βlnα)-approximation algorithm for SLS, where α is the independence number and β is the power diversity.