  Topology control, including topology construction and maintenance phases, is
a vital conception for wireless ad-hoc networks of any kind, expressly the
wireless sensor networks (WSN). Topology maintenance, the latter phase,
concerns several problems, such as optimizing the energy consumption,
increasing the data rate, making clusters, and sustaining the connectivity. A
disconnected network, among other strategies, can efficiently be connected
again using a Movement-based Connectivity Restoration (MCR) method, where a
commensurate number of nodes move (or are moved) to the desired positions.
However, finding an optimal route for the nodes to be moved can be a formidable
problem. As a matter of fact, this paper presents details regarding a direct
proof of the NP-Completeness of the MCR Problem by a reduction of the
well-studied Steiner Tree Problem using the minimum number of Steiner points
and the bounded edge length.
