{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T07:09:41Z","timestamp":1767856181737,"version":"3.49.0"},"reference-count":20,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2015,1,13]],"date-time":"2015-01-13T00:00:00Z","timestamp":1421107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"NSF","award":["CCF-0963921"],"award-info":[{"award-number":["CCF-0963921"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2015,1,13]]},"abstract":"<jats:p>\n            For an undirected\n            <jats:italic>n<\/jats:italic>\n            -vertex planar graph\n            <jats:italic>G<\/jats:italic>\n            with nonnegative edge weights, we consider the following type of query: given two vertices\n            <jats:italic>s<\/jats:italic>\n            and\n            <jats:italic>t<\/jats:italic>\n            in\n            <jats:italic>G<\/jats:italic>\n            , what is the weight of a min\n            <jats:italic>st<\/jats:italic>\n            -cut in\n            <jats:italic>G<\/jats:italic>\n            ? We show how to answer such queries in constant time with\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:sup>4<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            ) preprocessing time and\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>n<\/jats:italic>\n            ) space. We use a Gomory-Hu tree to represent all the pairwise min cuts implicitly. Previously, no subquadratic time algorithm was known for this problem. Since all-pairs min cut and the minimum-cycle basis are dual problems in planar graphs, we also obtain an implicit representation of a minimum-cycle basis in\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:sup>4<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            ) time and\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>n<\/jats:italic>\n            ) space. Additionally, an explicit representation can be obtained in\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>C<\/jats:italic>\n            ) time and space where\n            <jats:italic>C<\/jats:italic>\n            is the size of the basis.\n          <\/jats:p>\n          <jats:p>\n            These results require that shortest paths are unique. This can be guaranteed either by using randomization without overhead or deterministically with an additional log\n            <jats:sup>2<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            factor in the preprocessing times.\n          <\/jats:p>","DOI":"10.1145\/2684068","type":"journal-article","created":{"date-parts":[[2015,1,16]],"date-time":"2015-01-16T14:29:58Z","timestamp":1421418598000},"page":"1-29","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":17,"title":["Min\n            <i>st<\/i>\n            -Cut Oracle for Planar Graphs with Near-Linear Preprocessing Time"],"prefix":"10.1145","volume":"11","author":[{"given":"Glencora","family":"Borradaile","sequence":"first","affiliation":[{"name":"Oregon State University, Corvallis OR"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Piotr","family":"Sankowski","sequence":"additional","affiliation":[{"name":"University of Warsaw, Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Wulff-Nilsen","sequence":"additional","affiliation":[{"name":"University of Copenhagen, Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,1,13]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1103963.1103966"},{"key":"e_1_2_1_2_1","volume-title":"Proceedings of the 17th European Symposium on Algorithms (Lecture Notes in Computer Science), A. 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Sanders (Eds.). 301--312","author":"Amaldi E."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1250790.1250879"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcss.2005.05.007"},{"key":"e_1_2_1_5_1","first-page":"551","article-title":"Multi-terminal network flows","volume":"9","author":"Gomory R.","year":"1961","journal-title":"Journal of SIAM"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480190177042"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1493"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/0216026"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/0208012"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1993636.1993679"},{"key":"e_1_2_1_11_1","volume-title":"Lecture Notes in Computer Science","volume":"621","author":"Kant G."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-87744-8_47"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/andp.18471481202"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2488608.2488672"},{"key":"e_1_2_1_15_1","volume-title":"Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms. 146--155","author":"Klein P. 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