Two-Path Subsets: Efficient Counting and Applications to Performability Analysis

Abstract

The problem of computing preformability probabilities in stochastic PERT and flow networks is studied when the networks is ﲭinimally designed to withstand any two component failures. Polynomial-time algorithms to compute preformability when the network is planar -- the nonplanar versions being NP-hard -- solve related ﲴwo-path subset problems. Given an acyclic graph with weights on the arcs, the algorithms compute the total weight of all subsets of arcs that are contained in (1) two source-sink paths or (2) two arc-disjoint source-sink paths. A polynomial algorithm is given for (1), and for (2) in the case where the graph is a source-sink planar k-flow graph, that is edge-minimal with respect to supporting k units of flow.