2023/04/13 by Ruoxu Cen, Cen, Ruoxu, William He +5
Engineering · #Advanced Battery Technologies Research #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Power System Reliability and Maintenance #Reliability and Maintenance Optimization
paper · pdf · doi:10.48550/arxiv.2304.06552
openalex publication_date 2023/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Karger (STOC 1995) gave the first FPTAS for the network (un)reliability problem, setting in motion research over the next three decades that obtained increasingly faster running times, eventually leading to a O(n2)-time algorithm (Karger, STOC 2020). This represented a natural culmination of this line of work because the algorithmic techniques used can enumerate Θ(n2) (near)-minimum cuts. In this paper, we go beyond this quadratic barrier and obtain a faster FPTAS for the network unreliability problem. Our algorithm runs in m1+o(1) + O(n1.5) time. Our main contribution is a new estimator for network unreliability in very reliable graphs. These graphs are usually the bottleneck for network unreliability since the disconnection event is elusive. Our estimator is obtained by defining an appropriate importance sampling subroutine on a dual spanning tree packing of the graph. To complement this estimator for very reliable graphs, we use recursive contraction for moderately reliable graphs. We show that an interleaving of sparsification and contraction can be used to obtain a better parametrization of the recursive contraction algorithm that yields a faster running time matching the one obtained for the very reliable case.