{"year":"2018","title":"Incremental exact min-cut in polylogarithmic amortized update time","status":"public","intvolume":"        14","date_published":"2018-04-01T00:00:00Z","extern":"1","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."}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1611.06500"}],"type":"journal_article","author":[{"first_name":"Gramoz","full_name":"Goranci, Gramoz","last_name":"Goranci"},{"first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","last_name":"Henzinger"},{"last_name":"Thorup","first_name":"Mikkel","full_name":"Thorup, Mikkel"}],"_id":"11664","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"2","publication_status":"published","volume":14,"article_processing_charge":"No","month":"04","oa":1,"date_created":"2022-07-27T11:29:39Z","date_updated":"2024-11-06T12:05:51Z","acknowledgement":"We thank the two anonymous reviewers for their suggestions and comments, which improved the\r\nquality of the article.","doi":"10.1145/3174803","quality_controlled":"1","publication":"ACM Transactions on Algorithms","oa_version":"Preprint","article_number":"17","article_type":"original","day":"01","external_id":{"arxiv":["1611.06500"]},"scopus_import":"1","citation":{"short":"G. Goranci, M. Henzinger, M. Thorup, ACM Transactions on Algorithms 14 (2018).","apa":"Goranci, G., Henzinger, M., &#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>","ama":"Goranci G, Henzinger M, 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>","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>.","chicago":"Goranci, Gramoz, Monika 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>.","ieee":"G. Goranci, M. 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.","ista":"Goranci G, Henzinger M, Thorup M. 2018. Incremental exact min-cut in polylogarithmic amortized update time. ACM Transactions on Algorithms. 14(2), 17."},"publisher":"Association for Computing Machinery","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1549-6333"],"issn":["1549-6325"]},"arxiv":1}