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In this paper, we propose a general framework of the iterative local solution (ILS) for computing a connected dominating set (CDS) in ad hoc wireless networks, which include mobile ad hoc networks (MANETS) and wireless sensor networks (WSNs). This approach uses an iterative application of a selected local solution. Each application of the local solution enhances the result obtained from the previous iteration, but each is based on a different node priority scheme. Then, we integrate this iterative process into the process for handling a dynamic network topology and propose two extensions: cyclic iterative local solution (CILS) and seamless iterative local solution (SILS). CILS offers a natural extension of ILS to the dynamic environment but suffers from a broken CDS and nonadaptiveness. With a novel use of a monotonically increasing sequence number for dynamic node priority, SILS offers an extension with the desirable properties of correctness, progressiveness, locality, and seamlessness. Extensive simulations are conducted under ns-2 and a custom simulator to evaluate the effectiveness of the proposed approach in both static and dynamic environments.