  The binary-state network, a basic network, and its components are either
working or failed. It is fundamental to all types of current networks, such as
utility networks (gas, water, electricity, and 4G/5G), the Internet of Things
(IoT), social networks, and supply chains. Network reliability is an important
index in the planning, design, evaluation, and control of network systems, and
the minimal path (MC) is the basis of an MC-based algorithm for calculating
reliability. A new BAT called recursive node-based BAT is proposed and
implemented in a recursive manner such that the jth vector in the ith iteration
is equal to its parent, which is the jth vector, except that its ith coordinate
value is one. Based on time complexity analysis and experiments on 20 benchmark
binary-state networks, the proposed recursive node-based BAT is more efficient
than the best-known node-based algorithm in finding MCs when combined with
powerful rules to discard these infeasible vectors and all their offspring.
