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To derive the critical density for exposure-path prevention in three-dimensional wireless sensor networks (3D WSNs), a bond-percolation-based scheme is proposed, which can generate the tighter lower and upper bounds of critical density. Firstly, the exposure-path prevention problem and system models based on Gaussian distribution are introduced in this paper. Then, according to percolation theory, we present a bond-percolation model to put this problem into a 3D uniform lattice. With this model, the lower and upper bounds of critical density for 3D WSNs are derived in the light of our scheme. Extensive simulations and contrast experiments also validate our developed models and evaluate the performance of the proposed schemes. Therefore, our scheme can be applied to determine a practically reliable density and detect intruders in sensor networks.

Critical Density for Exposure-Path Prevention in Three-Dimensional Wireless Sensor Networks Using Percolation Theory