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Local flow partitioning for faster edge connectivity

Henzinger MH, Rao S, Wang D. 2020. Local flow partitioning for faster edge connectivity. SIAM Journal on Computing. 49(1), 1–36.

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Journal Article | Published | English

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Author
Henzinger, MonikaISTA ; Rao, Satish; Wang, Di
Abstract
We study the problem of computing a minimum cut in a simple, undirected graph and give a deterministic 𝑂(π‘šlog2𝑛loglog2𝑛) time algorithm. This improves on both the best previously known deterministic running time of 𝑂(π‘šlog12𝑛) (Kawarabayashi and Thorup [J. ACM, 66 (2018), 4]) and the best previously known randomized running time of 𝑂(π‘šlog3𝑛) (Karger [J. ACM, 47 (2000), pp. 46--76]) for this problem, though Karger's algorithm can be further applied to weighted graphs. Moreover, our result extends to balanced directed graphs, where the balance of a directed graph captures how close the graph is to being Eulerian. Our approach is using the Kawarabayashi and Thorup graph compression technique, which repeatedly finds low conductance cuts. To find these cuts they use a diffusion-based local algorithm. We use instead a flow-based local algorithm and suitably adjust their framework to work with our flow-based subroutine. Both flow- and diffusion-based methods have a long history of being applied to finding low conductance cuts. Diffusion algorithms have several variants that are naturally local, while it is more complicated to make flow methods local. Some prior work has proven nice properties for local flow-based algorithms with respect to improving or cleaning up low conductance cuts. Our flow subroutine, however, is the first that both is local and produces low conductance cuts. Thus, it may be of independent interest.
Publishing Year
Date Published
2020-01-01
Journal Title
SIAM Journal on Computing
Publisher
Society for Industrial & Applied Mathematics
Volume
49
Issue
1
Page
1-36
ISSN
eISSN
IST-REx-ID

Cite this

Henzinger MH, Rao S, Wang D. Local flow partitioning for faster edge connectivity. SIAM Journal on Computing. 2020;49(1):1-36. doi:10.1137/18m1180335
Henzinger, M. H., Rao, S., & Wang, D. (2020). Local flow partitioning for faster edge connectivity. SIAM Journal on Computing. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/18m1180335
Henzinger, Monika H, Satish Rao, and Di Wang. β€œLocal Flow Partitioning for Faster Edge Connectivity.” SIAM Journal on Computing. Society for Industrial & Applied Mathematics, 2020. https://doi.org/10.1137/18m1180335.
M. H. Henzinger, S. Rao, and D. Wang, β€œLocal flow partitioning for faster edge connectivity,” SIAM Journal on Computing, vol. 49, no. 1. Society for Industrial & Applied Mathematics, pp. 1–36, 2020.
Henzinger MH, Rao S, Wang D. 2020. Local flow partitioning for faster edge connectivity. SIAM Journal on Computing. 49(1), 1–36.
Henzinger, Monika H., et al. β€œLocal Flow Partitioning for Faster Edge Connectivity.” SIAM Journal on Computing, vol. 49, no. 1, Society for Industrial & Applied Mathematics, 2020, pp. 1–36, doi:10.1137/18m1180335.

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