{"abstract":[{"lang":"eng","text":"We study the problem of computing a minimum cut in a simple, undirected graph and give a deterministic 𝑂(𝑚log2𝑛loglog2𝑛) time algorithm. This improves on both the best previously known deterministic running time of 𝑂(𝑚log12𝑛) (Kawarabayashi and Thorup [J. ACM, 66 (2018), 4]) and the best previously known randomized running time of 𝑂(𝑚log3𝑛) (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."}],"publication":"SIAM Journal on Computing","publication_status":"published","related_material":{"record":[{"relation":"later_version","status":"public","id":"11873"}]},"author":[{"last_name":"Henzinger","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","full_name":"Henzinger, Monika H","first_name":"Monika H","orcid":"0000-0002-5008-6530"},{"full_name":"Rao, Satish","first_name":"Satish","last_name":"Rao"},{"last_name":"Wang","first_name":"Di","full_name":"Wang, Di"}],"doi":"10.1137/18m1180335","_id":"11889","publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"type":"journal_article","extern":"1","volume":49,"date_updated":"2023-02-21T16:31:25Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1704.01254"]},"page":"1-36","status":"public","date_created":"2022-08-17T08:09:31Z","month":"01","citation":{"ieee":"M. H. Henzinger, S. Rao, and D. Wang, “Local flow partitioning for faster edge connectivity,” <i>SIAM Journal on Computing</i>, vol. 49, no. 1. Society for Industrial &#38; Applied Mathematics, pp. 1–36, 2020.","ama":"Henzinger MH, Rao S, Wang D. Local flow partitioning for faster edge connectivity. <i>SIAM Journal on Computing</i>. 2020;49(1):1-36. doi:<a href=\"https://doi.org/10.1137/18m1180335\">10.1137/18m1180335</a>","mla":"Henzinger, Monika H., et al. “Local Flow Partitioning for Faster Edge Connectivity.” <i>SIAM Journal on Computing</i>, vol. 49, no. 1, Society for Industrial &#38; Applied Mathematics, 2020, pp. 1–36, doi:<a href=\"https://doi.org/10.1137/18m1180335\">10.1137/18m1180335</a>.","short":"M.H. Henzinger, S. Rao, D. Wang, SIAM Journal on Computing 49 (2020) 1–36.","apa":"Henzinger, M. H., Rao, S., &#38; Wang, D. (2020). Local flow partitioning for faster edge connectivity. <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/18m1180335\">https://doi.org/10.1137/18m1180335</a>","ista":"Henzinger MH, Rao S, Wang D. 2020. Local flow partitioning for faster edge connectivity. SIAM Journal on Computing. 49(1), 1–36.","chicago":"Henzinger, Monika H, Satish Rao, and Di Wang. “Local Flow Partitioning for Faster Edge Connectivity.” <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics, 2020. <a href=\"https://doi.org/10.1137/18m1180335\">https://doi.org/10.1137/18m1180335</a>."},"article_processing_charge":"No","oa_version":"Preprint","issue":"1","title":"Local flow partitioning for faster edge connectivity","quality_controlled":"1","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1704.01254"}],"language":[{"iso":"eng"}],"intvolume":"        49","date_published":"2020-01-01T00:00:00Z","day":"01","year":"2020","publisher":"Society for Industrial & Applied Mathematics","article_type":"original"}