Comparison of Binary and Multi-Variate Hybrid Decision Diagram Algorithms for K-Terminal Reliability

The Ordered Binary Decision Diagram (OBDD) has been efficiently used to compute the communication network (CN) reliability (REL). The boundary set method (BS) is used to improve the efficiency of the OBDD approach, while the augmented OBDD diagrams (OBDD-A) that stores CN information in its nodes has been proposed to solve other CN performance metrics in addition to REL. The hybrid OBDD (OBDD-H) combines the BS and OBDD-A features to further improve the performance of the OBDD method. However, both BS and OBDD-H address only CN with communication link (edge) failure. In this paper, we generalize OBDD-H for networks with edge and/or device (vertex) failures. We also present a hybrid ordered multi-variate decision diagram (OMDDH) to compute the performance metrics of CN with vertex and link failures. This paper examines the time and space complexities of OBDD-H, and shows that OMDD-H can compute the REL in CN with fallible vertices and edges in the same order of complexities as BS or OBDD-H computing the same network with only vertex failure .