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Wireless sensor networks receive lots of attention due to its promising techniques and wide-ranging applications in recent years. The kind of network occasionally becomes disconnected due to initial uneven deployments or unpredictable failures or run out of battery of sensor nodes. However, sensor nodes with mobility then can be used in an addition deployment to reconnect the disconnected sensor networks. Theoretically, the augmenting geometric graph problem is defined here to model this kind of connectivity issues. The work proposes two novel algorithms: the graph-oriented algorithm and the divide-and-conquer algorithm to connect disconnected networks by using as less as possible mobile nodes. The first algorithm highly exploits traditional graph and geometry techniques including Fermat point, convex hull, nearest neighbor, minimum cost spanning tree, and graph contraction. Adopting a quite different approach, the second algorithm resolves the problem by dividing the deployed area and merging sub-solutions recursively. With respect to complexity issue, the graph-oriented algorithm takes 0(n3) time; on the other hand, the divide-and-conquer algorithm requires 0(n log n) time, where n is the size of vertex set of the given graph G=(V, E). These proposed two algorithms have low time complexity and can be implemented in a centralized sensor network.