{"day":"01","scopus_import":"1","type":"journal_article","external_id":{"arxiv":["1611.06500"]},"publication":"ACM Transactions on Algorithms","_id":"11664","article_type":"original","status":"public","volume":14,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1145/3174803","date_updated":"2022-09-09T11:38:14Z","date_published":"2018-04-01T00:00:00Z","abstract":[{"lang":"eng","text":"We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with O(log3 n log log2 n) amortized time per edge insertion and O(1) query time. This result partially answers an open question posed by Thorup (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 sparsification technique of Kawarabayashi and Thorup (2015) or its recent improvement by Henzinger, Rao, and Wang (2017), and an exact incremental algorithm of Henzinger (1997).\r\n\r\nWe also study space-efficient incremental algorithms for the minimum cut problem. Concretely, we show that there exists an O(nlog n/ε2) 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+ε)-approximation to the minimum cut. The algorithm has O((α (n) log3 n)/ε 2) amortized update time and constant query time, where α (n) stands for the inverse of Ackermann function."}],"publication_identifier":{"issn":["1549-6325"],"eissn":["1549-6333"]},"issue":"2","oa_version":"Preprint","author":[{"full_name":"Goranci, Gramoz","first_name":"Gramoz","last_name":"Goranci"},{"orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","full_name":"Henzinger, Monika H","first_name":"Monika H","last_name":"Henzinger"},{"last_name":"Thorup","first_name":"Mikkel","full_name":"Thorup, Mikkel"}],"oa":1,"intvolume":"        14","article_processing_charge":"No","citation":{"mla":"Goranci, Gramoz, et al. “Incremental Exact Min-Cut in Polylogarithmic Amortized Update Time.” <i>ACM Transactions on Algorithms</i>, vol. 14, no. 2, 17, Association for Computing Machinery, 2018, doi:<a href=\"https://doi.org/10.1145/3174803\">10.1145/3174803</a>.","short":"G. Goranci, M.H. Henzinger, M. Thorup, ACM Transactions on Algorithms 14 (2018).","ama":"Goranci G, Henzinger MH, Thorup M. Incremental exact min-cut in polylogarithmic amortized update time. <i>ACM Transactions on Algorithms</i>. 2018;14(2). doi:<a href=\"https://doi.org/10.1145/3174803\">10.1145/3174803</a>","apa":"Goranci, G., Henzinger, M. H., &#38; Thorup, M. (2018). Incremental exact min-cut in polylogarithmic amortized update time. <i>ACM Transactions on Algorithms</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3174803\">https://doi.org/10.1145/3174803</a>","chicago":"Goranci, Gramoz, Monika H Henzinger, and Mikkel Thorup. “Incremental Exact Min-Cut in Polylogarithmic Amortized Update Time.” <i>ACM Transactions on Algorithms</i>. Association for Computing Machinery, 2018. <a href=\"https://doi.org/10.1145/3174803\">https://doi.org/10.1145/3174803</a>.","ista":"Goranci G, Henzinger MH, Thorup M. 2018. Incremental exact min-cut in polylogarithmic amortized update time. ACM Transactions on Algorithms. 14(2), 17.","ieee":"G. Goranci, M. H. Henzinger, and M. Thorup, “Incremental exact min-cut in polylogarithmic amortized update time,” <i>ACM Transactions on Algorithms</i>, vol. 14, no. 2. Association for Computing Machinery, 2018."},"year":"2018","extern":"1","article_number":"17","title":"Incremental exact min-cut in polylogarithmic amortized update time","date_created":"2022-07-27T11:29:39Z","main_file_link":[{"url":"https://arxiv.org/abs/1611.06500","open_access":"1"}],"publisher":"Association for Computing Machinery","quality_controlled":"1","acknowledgement":"We thank the two anonymous reviewers for their suggestions and comments, which improved the\r\nquality of the article.","publication_status":"published","language":[{"iso":"eng"}],"month":"04"}