An Improved General Upper Bound for All-Terminal Network Reliability

The exact calculation of all-terminal network reliability is an NP-hard problem, precluding its use in the design of optimal network topologies for problems of realistic size. This paper presents an improved upper bound for allterminal network reliability that is significantly more general than previously published bounds as it allows arcs of different reliabilities. The bound is calculated in polynomial time, making it computationally practical for large networks. The bound’s effectiveness is demonstrated on 108 network problems for both identical arc reliabilities and differing arc reliabilities. It is shown that the new bound yields statistically better results than a previously published bound with no increase in computational effort, and more importantly, the new bound can be used for network design problems that may include arcs with different reliabilities.