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In this paper, we explore the structures of the optimal solutions for the minimum power broadcast tree problem in wireless ad hoc networks. We investigate the common properties of the optimal solutions found by the algorithms based on integer programming and use the found features to describe the property of optimal solutions. We also present a series of theoretically rigorous study of the found property, named as incremental minimality. We provide the conditions of optimal solutions represented by the incrementally minimal transmissions. An algorithm based on the found properties is introduced and compared with other algorithms in the literature by computational experiments.