In this paper, we propose a distributed throughput-optimal ad hoc wireless network scheduling algorithm, which is motivated by the celebrated simplex algorithm for solving linear programming (LP) problems. The scheduler stores a sparse set of basic schedules, and chooses the max-weight basic schedule for transmission in each time slot. At the same time, the scheduler tries to update the set of basic schedules by searching for a new basic schedule in a throughput increasing direction. We show that both of the above procedures can be achieved in a distributed manner. Specifically, we propose an average consensus based link contending algorithm to implement the distributed max weight scheduling. Further, we show that the basic schedule update can be implemented using CSMA mechanisms, which is similar to the one proposed by Jiang et al. Compared to the optimal distributed scheduler, where schedules change in a random walk fashion, our algorithm has a better delay performance by achieving faster schedule transitions in the steady state. The performance of the algorithm is finally confirmed by simulation results.