{"article_number":"46","abstract":[{"text":"We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with ~O(1) amortized time per edge insertion and O(1) query time. This result partially answers an open question posed by Thorup [Combinatorica 2007]. It also stays in sharp contrast to a polynomial conditional lower-bound for the fully-dynamic weighted minimum cut problem. Our algorithm is obtained by combining a recent sparsification technique of Kawarabayashi and Thorup [STOC 2015] and an exact incremental algorithm of Henzinger [J. of Algorithm 1997].\r\n\r\nWe also study space-efficient incremental algorithms for the minimum cut problem. Concretely, we show that there exists an O(n log n/epsilon^2) space Monte-Carlo algorithm that can process a stream of edge insertions starting from an empty graph, and with high probability, the algorithm maintains a (1+epsilon)-approximation to the minimum cut. The algorithm has ~O(1) amortized update-time and constant query-time.","lang":"eng"}],"date_updated":"2023-02-16T12:05:59Z","language":[{"iso":"eng"}],"author":[{"full_name":"Goranci, Gramoz","first_name":"Gramoz","last_name":"Goranci"},{"full_name":"Henzinger, Monika H","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger","orcid":"0000-0002-5008-6530"},{"full_name":"Thorup, Mikkel","first_name":"Mikkel","last_name":"Thorup"}],"publisher":"Schloss Dagstuhl - Leibniz-Zentrum für Informatik","intvolume":"        57","scopus_import":"1","doi":"10.4230/LIPICS.ESA.2016.46","_id":"11834","alternative_title":["LIPIcs"],"conference":{"end_date":"2016-08-24","name":"ESA: Annual European Symposium on Algorithms","start_date":"2016-08-22","location":"Aarhus, Denmark"},"publication":"24th Annual European Symposium on Algorithms","external_id":{"arxiv":["1611.06500"]},"date_created":"2022-08-12T10:58:32Z","status":"public","citation":{"chicago":"Goranci, Gramoz, Monika H Henzinger, and Mikkel Thorup. “Incremental Exact Min-Cut in Poly-Logarithmic Amortized Update Time.” In <i>24th Annual European Symposium on Algorithms</i>, Vol. 57. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016. <a href=\"https://doi.org/10.4230/LIPICS.ESA.2016.46\">https://doi.org/10.4230/LIPICS.ESA.2016.46</a>.","ama":"Goranci G, Henzinger MH, Thorup M. Incremental exact min-cut in poly-logarithmic amortized update time. In: <i>24th Annual European Symposium on Algorithms</i>. Vol 57. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2016. doi:<a href=\"https://doi.org/10.4230/LIPICS.ESA.2016.46\">10.4230/LIPICS.ESA.2016.46</a>","short":"G. Goranci, M.H. Henzinger, M. Thorup, in:, 24th Annual European Symposium on Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016.","apa":"Goranci, G., Henzinger, M. H., &#38; Thorup, M. (2016). Incremental exact min-cut in poly-logarithmic amortized update time. In <i>24th Annual European Symposium on Algorithms</i> (Vol. 57). Aarhus, Denmark: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. <a href=\"https://doi.org/10.4230/LIPICS.ESA.2016.46\">https://doi.org/10.4230/LIPICS.ESA.2016.46</a>","ieee":"G. Goranci, M. H. Henzinger, and M. Thorup, “Incremental exact min-cut in poly-logarithmic amortized update time,” in <i>24th Annual European Symposium on Algorithms</i>, Aarhus, Denmark, 2016, vol. 57.","ista":"Goranci G, Henzinger MH, Thorup M. 2016. Incremental exact min-cut in poly-logarithmic amortized update time. 24th Annual European Symposium on Algorithms. ESA: Annual European Symposium on Algorithms, LIPIcs, vol. 57, 46.","mla":"Goranci, Gramoz, et al. “Incremental Exact Min-Cut in Poly-Logarithmic Amortized Update Time.” <i>24th Annual European Symposium on Algorithms</i>, vol. 57, 46, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016, doi:<a href=\"https://doi.org/10.4230/LIPICS.ESA.2016.46\">10.4230/LIPICS.ESA.2016.46</a>."},"day":"18","publication_status":"published","year":"2016","oa":1,"quality_controlled":"1","article_processing_charge":"No","publication_identifier":{"isbn":["978-3-95977-015-6"],"issn":["1868-8969"]},"title":"Incremental exact min-cut in poly-logarithmic amortized update time","volume":57,"oa_version":"Published Version","month":"08","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"conference","extern":"1","date_published":"2016-08-18T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.4230/LIPIcs.ESA.2016.46","open_access":"1"}]}