In this paper, we address the deployment problem for differentiated detection requirements, in which the required detection probability thresholds at different locations are different. We focus on differentiated deployment algorithms that are applied to the probabilistic detection model, since it is more realistic than the binary detection model. We show that the relationship between the node deployment strategy and the logarithmic collective miss probability distribution is Linear Shift Invariant (LSI). Using this property, we formulate the differentiated deployment problem as an integer linear programming problem, which is a well known NP-hard problem. We propose a differentiated node deployment algorithm called DIFF_DEPLOY, which achieves much better performance than the state-of-the-art node deployment algorithm for both uniform and differentiated detection requirements.
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