Determining terminal-pair reliability based on edge expansion diagrams using OBDD

Abstract

For calculating terminal-pair reliability, most published algorithms are based on the sum of disjoint products. However, these tree-based partitions lack the capability to avoid redundant computation due to the isomorphic sub-problems. To overcome these problems, an efficient methodology to evaluate the terminal-pair reliability, based on edge expansion diagrams using OBDD (ordered binary decision diagram) is presented. First, the success path function of a given network is constructed based on OBDD by traversing the network with diagram-based edge expansion. Then the reliability of the network is obtained by directly evaluating on this OBDD recursively. The effectiveness of this approach is demonstrated by performing experiments on benchmarks collected by previous works including the larger networks (from 4 to 2/sup 99/ paths). A dramatic improvement, as demonstrated by the experimental results for a 2-by-n lattice network is that the number of OBDD nodes is only linearly proportional to the number of stages, and is much better than previous algorithms which have exponential complexity by using the sum of disjoint products. The CPU time of reliability calculation for a 100-stage lattice network is only about 2.5 seconds with 595 nodes generated on a SPARC 20 workstation with 128 MBytes of memory. Thus, with this approach, the terminal-pair reliability of large networks can be efficiently evaluated better than thought possible.