Reliability Polynomial for Rectangular Lattice Strip

The study of graphs reliability polynomials is of both theoretical and practical interest. Generally, the problem of reliability polynomial calculation is NP-hard. In this paper we find analytic solution of this problem in some practical cases. Thus, linear complexity algorithm is offered for calculation of reliability of rectangular lattice strip. Graphs of this type can be used to model the topology of wireless sensor networks used to monitor long engineering infrastructure objects, such as pipeline systems. Sensors can be installed on the pipeline, inside it, or placed in the environment near the controlled object. To increase the efficiency of detecting events of interest, pairs of sensors operating on different physical principles can be used. By connecting paired sensors and neighboring homogeneous sensors with channels, we obtain a topology that is a rectangular lattice strip. However, this topology has advantages over linear sensor networks only if the channel reliability is high enough. Corresponding investigations have been presented in the paper.