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It is desirable for broadcast operation in wireless ad hoc network to prevent collision and achieve low latency at the same time. In this letter, we propose a greedy broadcast scheduling algorithm based on the graph theory of Maximum Weight Independent Set (MWIS) problem. During each broadcast wave cycle, MWIS is able to find the optimal selection of forwarders so that maximum number of untouched nodes is covered without incurring collision. Numerical results show that this algorithm could produce better performance results than recent 2-step approach.