Connectivity Matrices and Tree Search Strategy Based Wireless Sensor Networks Reliability Measures

This paper presents a matrix-based approach for evaluating <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{k}$</tex>-coverage probability and reliability in Wireless Sensor Networks (WSNs). The proposed method computes twoterminal reliability using connectivity matrices and recursive substitution operations, avoiding enumeration techniques. Exper- iments on various WSN configurations with different node and link densities demonstrate that the method provides continuous and tractable reliability estimates, outperforming standard SDP- based Hybrid Methods and SHARPE in certain cases. A compar- ative study highlights its advantages in computational complexity and accuracy. Future work could extend its applicability to dynamic networks by considering shadowing effects, energy constraints, and sensor heterogeneity.