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We consider the problem of transmission scheduling in wireless networks. A good transmission scheduling scheme should not only be conflict-free, in the sense of resolving collisions and the hidden terminal problem, but should also provide fairness and transmission efficiency to each node. We propose a class of scheduling schemes that rely on the logical ordering of the schedule update operations. The ordering is imposed by the precedence relationship of vertices in a directed acyclic graph (DAG). Two examples of establishing the logical DAG are given: (a) one relies on a distributed spanning tree construction; (b) one is based on location information. A separate mechanism ensures that nodes do not behave in a greedy fashion and monopolize the schedule slots. We prove the correctness of DAG-based schemes and provide simulation results that demonstrate their fairness and efficiency attributes.