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The scheduling problem in multi-hop wireless networks has been extensively investigated. Although throughput optimal scheduling solutions have been developed in the literature, they are unsuitable for multi-hop wireless systems because they are usually centralized and have very high complexity. In this paper, we develop a random-access based scheduling scheme that utilizes local information. The important features of this scheme include constant-time complexity, distributed operations, and a provable performance guarantee. Analytical results show that it guarantees a larger fraction of the optimal throughput performance than the state-of-the-art. Through simulations with both single-hop and multi-hop traffics, we observe that the scheme provides high throughput, close to that of a well-known highly efficient centralized greedy solution called the greedy maximal scheduler.