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In recent years, there has been a significant amount of work done in developing low-complexity scheduling schemes to achieve high performance in multihop wireless networks. A centralized suboptimal scheduling policy, called Greedy Maximal Scheduling (GMS) is a good candidate because its empirically observed performance is close to optimal in a variety of network settings. However, its distributed realization requires high complexity, which becomes a major obstacle for practical implementation. In this paper, we develop simple distributed greedy algorithms for scheduling in multihop wireless networks. We reduce the complexity by relaxing the global ordering requirement of GMS, up to near zero. Simulation results show that the new algorithms approximate the performance of GMS, and outperform the state-of-the-art distributed scheduling policies.