In the evaluation of the reliability of a multi-component system, the most important among several models fit into the class of stochastic graph models, for which an exact evaluation of reliability metrics is costly since these are classed in the NP-hard family As a consequence, many computation methods exist. This paper considers the all-terminal reliability measure R, which is extremely useful in the context of communication networks. It represents the probability that network nodes can exchange messages, taking into account possible failures of network components (nodes and links). The algorithm has the property of working with a bounded space, in fact, with space complexity linear in the size of the problem, an improvement over existing techniques which are exponential in space.