{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,20]],"date-time":"2024-08-20T09:07:51Z","timestamp":1724144871465},"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":"http:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"NSF","award":["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":"\n For an undirected\n n<\/jats:italic>\n -vertex planar graph\n G<\/jats:italic>\n with nonnegative edge weights, we consider the following type of query: given two vertices\n s<\/jats:italic>\n and\n t<\/jats:italic>\n in\n G<\/jats:italic>\n , what is the weight of a min\n st<\/jats:italic>\n -cut in\n G<\/jats:italic>\n ? We show how to answer such queries in constant time with\n O<\/jats:italic>\n (\n n<\/jats:italic>\n log\n 4<\/jats:sup>\n n<\/jats:italic>\n ) preprocessing time and\n O<\/jats:italic>\n (\n n<\/jats:italic>\n log\n 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 O<\/jats:italic>\n (\n n<\/jats:italic>\n log\n 4<\/jats:sup>\n n<\/jats:italic>\n ) time and\n O<\/jats:italic>\n (\n n<\/jats:italic>\n log\n n<\/jats:italic>\n ) space. Additionally, an explicit representation can be obtained in\n O<\/jats:italic>\n (\n C<\/jats:italic>\n ) time and space where\n C<\/jats:italic>\n is the size of the basis.\n <\/jats:p>\n \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 2<\/jats:sup>\n 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":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["Min\n 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"}]},{"given":"Piotr","family":"Sankowski","sequence":"additional","affiliation":[{"name":"University of Warsaw, Warsaw, Poland"}]},{"given":"Christian","family":"Wulff-Nilsen","sequence":"additional","affiliation":[{"name":"University of Copenhagen, Denmark"}]}],"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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