We study how to select and arrange multiple types of wireless sensors to build a star network that meets the coverage, the lifetime, the fault-tolerance, and the minimum-cost requirements, where the network lifetime, the acceptable failure probability of the network, and the failure rate of each type of sensors are given as parameters. This problem is NP-hard. We model this problem as an integer linear programming minimization problem. We then present an efficient approximation algorithm to find a feasible solution to the problem, which provides a sensor arrangement and a scheduling. We show that, through numerical experiments, our approximation provides solutions with approximation ratios less than 1.4.
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