{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T04:20:23Z","timestamp":1780546823730,"version":"3.54.1"},"reference-count":32,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T00:00:00Z","timestamp":1520812800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"Danish Council for Independent Research under the Sapere Aude research career programme","award":["DFF-0602-02499B"],"award-info":[{"award-number":["DFF-0602-02499B"]}]},{"name":"European Research Council under the European Union\u2019s 7th Framework Programme","award":["FP\/2007-2013"],"award-info":[{"award-number":["FP\/2007-2013"]}]},{"name":"ERC","award":["340506"],"award-info":[{"award-number":["340506"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2018,4,30]]},"abstract":"<jats:p>\n            We present a deterministic incremental algorithm for\n            <jats:italic>exactly<\/jats:italic>\n            maintaining the size of a minimum cut with\n            <jats:italic>O<\/jats:italic>\n            (log\n            <jats:sup>3<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            log log\n            <jats:sup>2<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            ) amortized time per edge insertion and\n            <jats:italic>O<\/jats:italic>\n            (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).\n          <\/jats:p>\n          <jats:p>\n            We also study space-efficient incremental algorithms for the minimum cut problem. Concretely, we show that there exists an\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>n<\/jats:italic>\n            \/\u03b5\n            <jats:sup>2<\/jats:sup>\n            ) 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+\u03b5)-approximation to the minimum cut. The algorithm has\n            <jats:italic>O<\/jats:italic>\n            ((\u03b1 (\n            <jats:italic>n<\/jats:italic>\n            ) log\n            <jats:sup>3<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            )\/\u03b5\n            <jats:sup>2<\/jats:sup>\n            ) amortized update time and constant query time, where \u03b1 (\n            <jats:italic>n<\/jats:italic>\n            ) stands for the inverse of Ackermann function.\n          <\/jats:p>","DOI":"10.1145\/3174803","type":"journal-article","created":{"date-parts":[[2018,3,12]],"date-time":"2018-03-12T12:49:54Z","timestamp":1520858994000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Incremental Exact Min-Cut in Polylogarithmic Amortized Update Time"],"prefix":"10.1145","volume":"14","author":[{"given":"Gramoz","family":"Goranci","sequence":"first","affiliation":[{"name":"University of Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Monika","family":"Henzinger","sequence":"additional","affiliation":[{"name":"University of Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mikkel","family":"Thorup","sequence":"additional","affiliation":[{"name":"University of Copenhagen, Copenhagen East, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2018,3,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2014.53"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02930-1_27"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/2213556.2213560"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/070705970"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2746539.2746592"},{"key":"e_1_2_1_6_1","volume-title":"Introduction to Algorithms","author":"Cormen Thomas H.","unstructured":"Thomas H. Cormen , Charles E. Leiserson , Ronald L. Rivest , and Clifford Stein . 2009. Introduction to Algorithms ( 3 rd ed.). MIT Press , Cambridge, MA . Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2009. Introduction to Algorithms (3rd ed.). MIT Press, Cambridge, MA.","edition":"3"},{"key":"e_1_2_1_7_1","first-page":"290","article-title":"On the structure of a family of minimum weighted cuts in a graph","volume":"1976","author":"Dinitz E. A.","year":"1976","unstructured":"E. A. Dinitz , A. V. Karzanov , and M. V. Lomonosov . 1976 . On the structure of a family of minimum weighted cuts in a graph . Studies in Discrete Optimization 1976 , 290 -- 306 . E. A. Dinitz, A. V. Karzanov, and M. V. Lomonosov. 1976. On the structure of a family of minimum weighted cuts in a graph. Studies in Discrete Optimization 1976, 290--306.","journal-title":"Studies in Discrete Optimization"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009195"},{"key":"e_1_2_1_9_1","volume-title":"Retrieved","author":"Fleiner Tam\u00e1s","year":"2009","unstructured":"Tam\u00e1s Fleiner and Andr\u00e1s Frank . 2009 . A quick proof for the cactus representation of mincuts . Retrieved February 10, 2018, from http:\/\/web.cs.elte.hu\/&sim;frank\/cikkek\/FrankR3.pdf. Tam\u00e1s Fleiner and Andr\u00e1s Frank. 2009. A quick proof for the cactus representation of mincuts. Retrieved February 10, 2018, from http:\/\/web.cs.elte.hu\/&sim;frank\/cikkek\/FrankR3.pdf."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1991.185453"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1995.1022"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/0222002"},{"key":"e_1_2_1_13_1","unstructured":"David Gibb Bruce M. Kapron Valerie King and Nolan Thorn. 2015. Dynamic graph connectivity with improved worst case update time and sublinear space. arXiv:1509.06464.  David Gibb Bruce M. Kapron Valerie King and Nolan Thorn. 2015. Dynamic graph connectivity with improved worst case update time and sublinear space. arXiv:1509.06464."},{"key":"e_1_2_1_14_1","volume-title":"Proceedings of the 24th European Symposium on Algorithms (ESA\u201916)","author":"Goranci Gramoz","year":"2016","unstructured":"Gramoz Goranci , Monika Henzinger , and Mikkel Thorup . 2016 . Incremental exact min-cut in poly-logarithmic amortized update time . In Proceedings of the 24th European Symposium on Algorithms (ESA\u201916) . 46:1--46:17. Gramoz Goranci, Monika Henzinger, and Mikkel Thorup. 2016. Incremental exact min-cut in poly-logarithmic amortized update time. In Proceedings of the 24th European Symposium on Algorithms (ESA\u201916). 46:1--46:17."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/2746539.2746609"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.5555\/3039686.3039811"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1997.0855"},{"key":"e_1_2_1_19_1","volume-title":"Proceedings of the 5th Symposium on Discrete Algorithms (SODA\u201994)","author":"Karger David R.","year":"1994","unstructured":"David R. Karger . 1994 . Using randomized sparsification to approximate minimum cuts . In Proceedings of the 5th Symposium on Discrete Algorithms (SODA\u201994) . 424--432. David R. Karger. 1994. Using randomized sparsification to approximate minimum cuts. In Proceedings of the 5th Symposium on Discrete Algorithms (SODA\u201994). 424--432."},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.24.2.383"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/331605.331608"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/2746539.2746588"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-012-9396-1"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.5555\/3039686.3039818"},{"key":"e_1_2_1_25_1","volume-title":"Proceedings of the 19th European Symposium on Algorithms (ESA\u201911)","author":"Lacki Jakub","year":"2011","unstructured":"Jakub Lacki and Piotr Sankowski . 2011 . Min-cuts and shortest cycles in planar graphs in O(n log log n) time . In Proceedings of the 19th European Symposium on Algorithms (ESA\u201911) . 155--166. Jakub Lacki and Piotr Sankowski. 2011. Min-cuts and shortest cycles in planar graphs in O(n log log n) time. In Proceedings of the 19th European Symposium on Algorithms (ESA\u201911). 155--166."},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm-10-1-96-115"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01758778"},{"key":"e_1_2_1_28_1","volume-title":"Algorithmic Aspects of Graph Connectivity","author":"Nagamochi Hiroshi","unstructured":"Hiroshi Nagamochi and Toshihide Ibaraki . 2008. Algorithmic Aspects of Graph Connectivity . Cambridge University Press , New York, NY . Hiroshi Nagamochi and Toshihide Ibaraki. 2008. Algorithmic Aspects of Graph Connectivity. Cambridge University Press, New York, NY."},{"key":"e_1_2_1_29_1","unstructured":"Danupon Nanongkai and Thatchaphol Saranurak. 2016. Dynamic cut oracle. Under submission.  Danupon Nanongkai and Thatchaphol Saranurak. 2016. Dynamic cut oracle. Under submission."},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793257770"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(83)90006-5"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00493-007-0045-2"},{"key":"e_1_2_1_33_1","volume-title":"Proceedings of the 7th Scandinavian Workshop on Algorithm Theory. 1--9.","author":"Thorup Mikkel","unstructured":"Mikkel Thorup and David R. Karger . 2000. Dynamic graph algorithms with applications . In Proceedings of the 7th Scandinavian Workshop on Algorithm Theory. 1--9. Mikkel Thorup and David R. Karger. 2000. Dynamic graph algorithms with applications. In Proceedings of the 7th Scandinavian Workshop on Algorithm Theory. 1--9."}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3174803","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3174803","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T02:11:33Z","timestamp":1750212693000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3174803"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,12]]},"references-count":32,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2018,4,30]]}},"alternative-id":["10.1145\/3174803"],"URL":"https:\/\/doi.org\/10.1145\/3174803","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"value":"1549-6325","type":"print"},{"value":"1549-6333","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,12]]},"assertion":[{"value":"2016-11-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-12-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-03-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}