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In most applications involving wireless sensor networks (WSN), each sensor equipped with a battery collects data in the surrounding area, and forwards it for processing. Since the battery is irreplaceable, many researchers have investigated the issue of extending the network lifetime by reducing the total energy consumption by the network. A possible solution is to construct a backbone of a reasonable size for the network that consumes as little energy as possible. A common approach to construct a backbone for a WSN is to build a set of nodes such that every other node is close to a node in this set. Such a set is known as a dominating set in graph theory. In this paper, we study the problem of assigning minimum total power to a set of nodes in the plane yielding a graph containing a connected d-hop dominating set of bounded size. We prove that this problem is NP-complete. We also introduce several heuristics for this problem and discuss their performance through simulations.