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Considering a communication topology of a wireless network modeled by a graph where an edge exists between two nodes if they are within each other's communication range. A subset U of nodes is a dominating set if each node is either in U or adjacent to some node in U. Assume each node has a disparate communication range and is associated with a positive weight, we present a randomized algorithm to find a min-weight dominating set. Considering any orientation of the graph where an arc uv existsarXiv:1208.5738v1 fatcat:v7kbyz2hczfkvn2hubcegbhc2m