A Fast and Exact Evaluation Algorithm for the Expected Number of Connected Nodes: an Enhanced Network Reliability Measure.

Contemporary society survives on several network infrastructures, such as communication and transportation. These network infrastructures are required to keep all nodes connected, although these nodes are occasionally disconnected due to failures. Thus, the expected number of connected node pairs (ECP) during an operation period is a reasonable reliability measure in network design. However, no work has studied ECP due to its computational hardness; we have to solve the reliability evaluation problem, which is a computationally tough problem, for O(n ² ) times where n is the number of nodes in a network. This paper proposes an efficient method that exactly computes ECP. Our method performs dynamic programming just once without explicit repetition for each node pair and obtains an exact ECP value weighted by the number of users at each node. A thorough complexity analysis reveals that our method is faster than an existing reliability evaluation method, which can be transferred to ECP computation, by O(n). Numerical experiments using real topologies show great efficiency; e.g., our method computes the ECP of an 821-link network in ten seconds; the existing method cannot complete it in an hour. This paper also presents two applications: critical link identification and optimal resource (e.g., a server) placement.