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We consider the problem of relocating a sensor node in its neighborhood so that the connectivity of the network is not altered. In this context, we introduce the notion of \in-free and out-free regions to capture the set of points where the node can be relocated by conserving connectivity. We present a characterization of maximal free-regions that can be used for identifying the position where the node can be moved to increase the reliability of the network connectivity. In addition, we prove that the free-region computation problem has a lower bound \(\Omega(n\log n)\) in the comparison tree model of computation, and also present two approximation algorithms for computing the free region of a sensor node in time \(O(k)\) and \(O(k\log k)\).