Cumulative Update of All-Terminal Reliability for Faster Feasibility Decision

Designing a reliable network becomes a time-consuming task if it involves All-Terminal Reliability (ATR) calculation, which belongs to the class of NP-hard problems. To make this task easier to address, we propose a new algorithm to decide the ATR feasibility of a given network G without performing exhaustive calculation. The proposed algorithm cumulatively updates the lower and upper bounds of the ATR using the set of subnetworks decomposed or branched from G. Once the lower or upper bound reaches the predetermined ATR requirement, the feasibility of G is determined. The proposed algorithm is characterized by four existing ATR calculation methods, which decompose or branch G into multiple subnetworks. The four implementations of the proposed algorithm will be tested via computer experiments. The results show that the proposed algorithm can make feasibility decision dramatically faster. The arrangement of subnetworks that can improve the performance of the proposed algorithm is also discussed.