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The performance of scheduling schemes in multi-hop wireless networks has attracted significant attention in the recent literature. It is well known that optimal scheduling solutions require centralized information and lead to impractical implementations due to their enormous complexity (high-degree polynomial or NP-hard, depending on the interference scenario). Further, multi-hop networks typically require distributed algorithms that operate on local information. Thus, in this paper, we develop a constant-time distributed random access algorithm for scheduling in multi-hop wireless networks. An important feature of this scheme is that it is guaranteed to achieve a fraction (efficiency factor) of the optimal performance. We show that this scheme theoretically achieves a superior efficiency factor as well as numerically achieves a significant performance improvement over the state-of-the-art. Simulation results also confirm that the performance of this scheme is close to a greedy centralized scheme.