Efficient and Exact Algorithm for All Pair-Wise Network Reliability and Its Applications to Enhance Unreliable Pairs

Kengo Nakamura, Takeru Inoue, Masaaki Nishino, Norihito Yasuda

Abstract: Modern society is underpinned by several network infrastructures, such as telecommunications and transportation. In these network infrastructures, every node pair should remain connected even if some network components fail. Thus, network operators must accurately evaluate the reliability between each node pair and effectively enhance unreliable pairs. Unfortunately, network reliability evaluation is known to be computationally difficult even for a single pair, and no accurate and efficient algorithm for all pairs has been developed. This paper introduces the problem of 2-NR++, evaluating network reliability for all node pairs, and proposes an efficient and exact algorithm. Unlike the previous algorithms, the proposed algorithm constructs only one data structure to compute the reliability of all node pairs. Numerical evaluation using real network benchmarks shows that our algorithm is faster than the state-of-the-art by an order of magnitude; e.g., our algorithm solves 2-NR++ in less than one hour even for a large network with 240 nodes, whereas the state-of-the-art requires more than one day. As an application of our algorithm, we also introduce a link augmentation problem to improve the least unreliable pair. We demonstrate that our algorithm reduces the computation time by around 30–90 times compared to the state-of-the-art.