Pseudopolynomial algorithms for calculating reliability

Abstract

Abstract As discussed in previous chapters, the calculation of reliability is known to be #P-complete, meaning that there is unlikely to exist an algorithm that is polynomial in the size of the input network (the number of nodes and the number of edges). Part of the difficulty inherent in reliability calculations is the fact that the number of simple paths and cutsets in a network can grow exponentially with its size. Thus the techniques of inclusion-exclusion and disjoint products, as well as other methods that process a given listing of the paths or cutsets, are automatically doomed to exponential growth in the worst case. A less ambitious, but still important, objective is to seek pseudopolynomial algorithms for calculating network reliability-methods that are polynomially bounded in the number of simple paths or the number of cutsets. Since there exist methods, described in Chapter 5, that allow the paths and cutsets to be generated efficiently in terms of the number of such objects, subsequent processing of these objects by a pseudopolynomial algorithm might be effective in cases where the number of such objects is not too large.