Edge-Packings of Graphs and Network Reliability

The reliability of a network can be efficiently bounded using graph-theoretical techniques based on edge-packing. We examine the application of combinatorial theorems on edgepacking spanning trees, s, t-paths, and s, t-cuts to the determination of reliability bounds. The application of spanning trees has been studied by Polesskii, and the application of s, t-paths has been studied by Brecht and Colbourn. The use of edge-packings of s, t-cutsets has not been previously examined. We compare the resulting bounds with known bounds produced by different techniques, and establish that the edge-packing bounds often produce a substantial improvement. We also establish that three other edge-packing problems arising in reliability bounding are NP-complete, namely edge-packing by network cutsets, Steiner trees, and Steiner cutsets.