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In this paper, we investigate the power-efficient broadcast routing problem over heterogeneous wireless ad hoc or sensor networks where network nodes have a heterogeneous capability. The network links between pairs of nodes can no longer be modeled as symmetric or bidirectional. We show that, while most previous power-efficient algorithms work in this setting with minor modifications, they are not designed to exploit such asymmetric constraints. We present a suitable algorithm which takes into account the constraints and yet is the most power-efficient among all known algorithms.