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Beyond the Quadratic Time Barrier for Network Unreliability

Publication ,  Conference
Cen, R; He, W; Li, J; Panigrahi, D
Published in: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
January 1, 2024

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 Õ(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) + Õ(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.

Duke Scholars

Published In

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

DOI

Publication Date

January 1, 2024

Volume

2024-January

Start / End Page

1542 / 1567
 

Citation

APA
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ICMJE
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Cen, R., He, W., Li, J., & Panigrahi, D. (2024). Beyond the Quadratic Time Barrier for Network Unreliability. In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms (Vol. 2024-January, pp. 1542–1567). https://doi.org/10.1137/1.9781611977912.62
Cen, R., W. He, J. Li, and D. Panigrahi. “Beyond the Quadratic Time Barrier for Network Unreliability.” In Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, 2024-January:1542–67, 2024. https://doi.org/10.1137/1.9781611977912.62.
Cen R, He W, Li J, Panigrahi D. Beyond the Quadratic Time Barrier for Network Unreliability. In: Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. 2024. p. 1542–67.
Cen, R., et al. “Beyond the Quadratic Time Barrier for Network Unreliability.” Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 2024-January, 2024, pp. 1542–67. Scopus, doi:10.1137/1.9781611977912.62.
Cen R, He W, Li J, Panigrahi D. Beyond the Quadratic Time Barrier for Network Unreliability. Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms. 2024. p. 1542–1567.

Published In

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

DOI

Publication Date

January 1, 2024

Volume

2024-January

Start / End Page

1542 / 1567