We study the coverage and connectivity problem in wireless sensor networks. Given an area of targets to cover by a wireless sensor network with a coverage range for each sensor, the problem consists in minimizing the number of deployed sensors in an area while ensuring the connectivity of the sensors network and the coverage of the area. We formulate the problem by a binary integer programming model to minimize the total number of used sensors. Since the problem is NP-complete, firstly we design a separation oracle to establish the feasibility of each solution. Then we provide an iterative approximation based on combinatorial relaxation.
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