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Database Syst."],"published-print":{"date-parts":[[2020,9,30]]},"abstract":"We consider the problem of incrementally maintaining the triangle queries with arbitrary free variables under single-tuple updates to the input relations.<\/jats:p>\n We introduce an approach called IVM\u03f5 that exhibits a trade-off between the update time, the space, and the delay for the enumeration of the query result, such that the update time ranges from the square root to linear in the database size while the delay ranges from constant to linear time.<\/jats:p>\n IVM\u03f5 achieves Pareto worst-case optimality in the update-delay space conditioned on the Online Matrix-Vector Multiplication conjecture. It is strongly Pareto optimal for the triangle queries with no or three free variables and weakly Pareto optimal for the remaining triangle queries with one or two free variables.<\/jats:p>\n IVM\u03f5 recovers prior work such as the suboptimal classical view maintenance approach that uses delta query processing and the worst-case optimal approach that computes all triangles in a static database.<\/jats:p>","DOI":"10.1145\/3396375","type":"journal-article","created":{"date-parts":[[2020,7,7]],"date-time":"2020-07-07T12:33:48Z","timestamp":1594125228000},"page":"1-46","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Maintaining Triangle Queries under Updates"],"prefix":"10.1145","volume":"45","author":[{"given":"Ahmet","family":"Kara","sequence":"first","affiliation":[{"name":"University of Zurich, Switzerland"}]},{"given":"Hung Q.","family":"Ngo","sequence":"additional","affiliation":[{"name":"RelationalAI, Inc., Berkeley, CA"}]},{"given":"Milos","family":"Nikolic","sequence":"additional","affiliation":[{"name":"University of Edinburgh, Edinburgh, UK"}]},{"given":"Dan","family":"Olteanu","sequence":"additional","affiliation":[{"name":"University of Zurich, Switzerland"}]},{"given":"Haozhe","family":"Zhang","sequence":"additional","affiliation":[{"name":"University of Oxford, Oxford, UK"}]}],"member":"320","published-online":{"date-parts":[[2020,8,26]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2014.53"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/2902251.2902280"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02523189"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.5555\/545381.545464"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1839490.1839494"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/3034786.3034789"},{"key":"e_1_2_2_7_1","first-page":"1","article-title":"Answering UCQs under updates and in the presence of integrity constraints","volume":"8","author":"Berkholz Christoph","year":"2018","unstructured":"Christoph Berkholz , Jens Keppeler , and Nicole Schweikardt . 2018 . 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