{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T05:53:20Z","timestamp":1763704400781},"reference-count":15,"publisher":"Association for Computing Machinery (ACM)","issue":"3","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2006,7]]},"abstract":"<jats:p>\n            It is shown that the problem of maintaining the topological order of the nodes of a directed acyclic graph while inserting\n            <jats:italic>m<\/jats:italic>\n            edges can be solved in\n            <jats:italic>O<\/jats:italic>\n            (min{\n            <jats:italic>m<\/jats:italic>\n            <jats:sup>3\/2<\/jats:sup>\n            log\n            <jats:italic>n<\/jats:italic>\n            ,\n            <jats:italic>m<\/jats:italic>\n            <jats:sup>3\/2<\/jats:sup>\n            +\n            <jats:italic>n<\/jats:italic>\n            <jats:sup>2<\/jats:sup>\n            log\n            <jats:italic>n<\/jats:italic>\n            }) time, an improvement over the best known result of\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>mn<\/jats:italic>\n            ). In addition, we analyze the complexity of the same algorithm with respect to the treewidth\n            <jats:italic>k<\/jats:italic>\n            of the underlying undirected graph. We show that the algorithm runs in time\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>mk<\/jats:italic>\n            log\n            <jats:sup>2<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            ) for general\n            <jats:italic>k<\/jats:italic>\n            and that it can be implemented to run in\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:italic>n<\/jats:italic>\n            ) time on trees, which is optimal. The algorithm also detects cycles in the input.\n          <\/jats:p>","DOI":"10.1145\/1159892.1159896","type":"journal-article","created":{"date-parts":[[2006,10,18]],"date-time":"2006-10-18T18:11:32Z","timestamp":1161195092000},"page":"364-379","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":13,"title":["Online topological ordering"],"prefix":"10.1145","volume":"2","author":[{"given":"Irit","family":"Katriel","sequence":"first","affiliation":[{"name":"BRICS, University of Aarhus, \u00c5rhus, Denmark"}]},{"given":"Hans L.","family":"Bodlaender","sequence":"additional","affiliation":[{"name":"Utrecht University, Utrecht, The Netherlands"}]}],"member":"320","published-online":{"date-parts":[[2006,7]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"SODA '90: Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics","author":"Alpern B."},{"key":"e_1_2_1_2_1","volume-title":"ESA '02: Proceedings of the 10th Annual European Symposium on Algorithms","author":"Bender M. A."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(97)00228-4"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/28395.28434"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/28869.28874"},{"key":"e_1_2_1_6_1","unstructured":"Katriel I. 2004. On algorithms for online topological ordering and sorting. Res. Rep. MPI-I-2004-1-003 Max-Planck-Institut f\u00fcr Informatik Saarbr\u00fccken Germany.  Katriel I. 2004. On algorithms for online topological ordering and sorting. Res. Rep. MPI-I-2004-1-003 Max-Planck-Institut f\u00fcr Informatik Saarbr\u00fccken Germany."},{"key":"e_1_2_1_7_1","volume-title":"WG '93: Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science","author":"Marchetti-Spaccamela A."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(96)00075-0"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/582419.582430"},{"key":"e_1_2_1_10_1","volume-title":"Tech. Rep. TR-92-017","author":"Omohundro S.","year":"1992"},{"key":"e_1_2_1_11_1","volume-title":"Proceedings of the Workshop on Efficient and Experimental Algorithms. Lecture Notes in Computer Science","volume":"3059","author":"Pearce D. J."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(94)00080-8"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(95)00079-8"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(86)90023-4"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/0201010"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1159892.1159896","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T20:42:37Z","timestamp":1672260157000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1159892.1159896"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,7]]}},"alternative-id":["10.1145\/1159892.1159896"],"URL":"https:\/\/doi.org\/10.1145\/1159892.1159896","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"value":"1549-6325","type":"print"},{"value":"1549-6333","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,7]]},"assertion":[{"value":"2006-07-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}