Abstract
A simplified model for a communication network is a probabilistic graph where no node fails but each edge operates with a probability. One of the indicators which measure the performance of the network is all-terminal reliability, that is, the probability that all nodes are connected with operational edges. Since it is #P-complete to calculate the value of the all-terminal reliability precisely, it is important to obtain its bound efficiently. In [29], we have proposed a polynomial time algorithm that derives the lower bound by using edge-packing consisting of spanning trees. They have a great merit that they can be applied to the probabilistic graphs where each edge operates with a different probability. In this paper, we propose new algorithms by using edge-packing consisting of series-parallel subgraphs. The algorithms derive tighter lower bounds without losing the above merit.
