Network reliability algorithms which produce sums of disjoint products (SDP) are sensitive to the order in which the minimal pathsets are analyzed. The minpaths are preprocessed by choosing this order in the hope that an SDP algorithm will then provide a relatively efficient analysis. The most commonly used preprocessing strategy is to list the minpaths in order of increasing size. This paper gives examples for which this strategy is not optimal. A new preprocessing strategy which works well for SDP algorithms with single-variable inversion (SVI) is introduced. It is also observed that optimal preprocessing for SVI-SDP can be different from optimal preprocessing for SDP algorithms which use multiple-variable inversion; one reason for this is that MVI-SDP algorithms handle disjoint minpaths much more effectively than SVI-SDP algorithms do. Both kinds of SDP algorithms profit from prior reduction of elements and of subsystems which are in parallel or in series.

The author comments on the paper by L.B. Page et al., (see ibid., vol.43, p.51-8, 1994). The author considers the reliability of a communication network, represented by a graph G of nodes and edges (also called "links"); the nodes are assumed to be perfectly operational and the edges are assumed to be Y-independently operational with probability p. He points out the redundancy. The original author replies to the comment.

The (K, j)-reliability of a K-terminal network G is the probability that after the failure of some of its edges the vertices in K will lie in no more than j connected components of the resulting subnetwork of G; when j = 1, this is the usual K-terminal reliability of G. In this paper, we extend the well-known theory of reliability domination and its application to the analysis of factoring algorithms for the computation of K-terminal reliability to (K, j)-reliability and the associated notion of (K, j)-domination. We give conditions equivalent to two edges being parallel or in series with respect to (K, j)-reliability, and we characterize the networks of (K, j)-domination ≥ 3. © 1997 John Wiley & Sons, Inc. Networks 30: 293–306, 1997

Abstract Lehman observed that star—delta and delta—star transformation cannot always be applied to networks with perfect (unfailing) vertices so as to exactly preserve reliability, and Rosenthal and Frisque introduced imperfect vertices to make exact delta—star transformations possible. We give an explicit condition that is satisfied if and only if a network with perfect vertices can be subjected to an exact star—delta or delta—star transformation, and we discuss the introduction of imperfect faces to make exact star—delta transformations possible. © 1993 by John Wiley & Sons, Inc.