The Evaluations on Lower Bounds of All-Terminal Reliability by Arc-Packings for General Networks

All-terminal reliability is one of the measurements to evaluate the reliability for network systems. Since it may need exponential time of the network size to compute the exact value of all-terminal reliability, it is important to calculate its tight approximate value, especially its lower bound, at a moderate calculation time. Ramanathan and Colbourn have proposed approaches for lower bounds of all-terminal reliability by using arc-packings but their approaches are not detailed enough to construct concrete algorithms and they have just evaluated their approaches for a particular network. In this paper, we construct concrete algorithms based on their approaches and suggest new algorithms. We also execute computational experiments for general networks in order to evaluate the lower bounds by the algorithms and show the effectiveness of our new algorithms. key words: probabilistic graph, network reliability, arc-packing, acyclic graph, lower bound