{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:32:31Z","timestamp":1750307551907,"version":"3.41.0"},"reference-count":12,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2010,3,1]],"date-time":"2010-03-01T00:00:00Z","timestamp":1267401600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2010,3]]},"abstract":"<jats:p>\n            In this work, we are interested in periodic trends in long data streams in the presence of computational constraints. To this end; we present algorithms for discovering periodic trends in the combinatorial property testing model in a data stream\n            <jats:italic>S<\/jats:italic>\n            of length\n            <jats:italic>n<\/jats:italic>\n            using\n            <jats:italic>o<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            ) samples and space.\n          <\/jats:p>\n          <jats:p>\n            In accordance with the property testing model, we first explore the notion of being \u201cclose\u201d to periodic by defining three different notions of self-distance through relaxing different notions of exact periodicity. An input\n            <jats:italic>S<\/jats:italic>\n            is then called approximately periodic if it exhibits a small self-distance (with respect to any one self-distance defined). We show that even though the different definitions of exact periodicity are equivalent, the resulting definitions of self-distance and approximate periodicity are not; we also show that these self-distances are constant approximations of each other. Afterwards, we present algorithms which distinguish between the two cases where\n            <jats:italic>S<\/jats:italic>\n            is exactly periodic and\n            <jats:italic>S<\/jats:italic>\n            is far from periodic with only a constant probability of error.\n          <\/jats:p>\n          <jats:p>\n            Our algorithms sample only\n            <jats:italic>O<\/jats:italic>\n            (\u221a\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:sup>2<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            ) (or\n            <jats:italic>O<\/jats:italic>\n            (\u221a\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:sup>4<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            ), depending on the self-distance) positions and use as much space. They can also find, using\n            <jats:italic>o<\/jats:italic>\n            (\n            <jats:italic>n<\/jats:italic>\n            ) samples and space, the largest\/smallest period, and\/or all of the approximate periods of\n            <jats:italic>S<\/jats:italic>\n            . These algorithms can also be viewed as working on streaming inputs where each data item is seen once and in order, storing only a sublinear (\n            <jats:italic>O<\/jats:italic>\n            (\u221a\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:sup>2<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            ) or\n            <jats:italic>O<\/jats:italic>\n            (\u221a\n            <jats:italic>n<\/jats:italic>\n            log\n            <jats:sup>4<\/jats:sup>\n            <jats:italic>n<\/jats:italic>\n            )) size sample from which periodicities are identified.\n          <\/jats:p>","DOI":"10.1145\/1721837.1721859","type":"journal-article","created":{"date-parts":[[2010,4,7]],"date-time":"2010-04-07T02:56:32Z","timestamp":1270608992000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Periodicity testing with sublinear samples and space"],"prefix":"10.1145","volume":"6","author":[{"given":"Funda","family":"Ergun","sequence":"first","affiliation":[{"name":"Simon Fraser University, Burnaby, BC, Canada"}]},{"given":"S.","family":"Muthukrishnan","sequence":"additional","affiliation":[{"name":"Google Research, New York, NY"}]},{"given":"Cenk","family":"Sahinalp","sequence":"additional","affiliation":[{"name":"Simon Fraser University, Burnaby, BC, Canada"}]}],"member":"320","published-online":{"date-parts":[[2010,4,6]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/780542.780590"},{"volume-title":"Proceedings of the 17th Conference on Data Engineering (ICDE). IEEE Computer Society Press","author":"Chaudhuri S.","key":"e_1_2_1_2_1"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.5555\/647819.736205"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/349093.349108"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1965-0174934-9"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/509907.509933"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/285055.285060"},{"volume-title":"Proceedings of the 26th International Conference on Very Large Data Bases (VLDB). ACM","author":"Indyk P.","key":"e_1_2_1_8_1"},{"key":"e_1_2_1_9_1","unstructured":"Kollios G. 2001. Time series indexing. http:\/\/www.cs.bu.edu\/faculty\/gkollios\/ada01\/LectNotes\/tsindexing.ppt.  Kollios G. 2001. Time series indexing. http:\/\/www.cs.bu.edu\/faculty\/gkollios\/ada01\/LectNotes\/tsindexing.ppt."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/11538462_31"},{"key":"e_1_2_1_11_1","unstructured":"Olken F. and Rotem D. 1993. Random sampling from databases: A survey. http:\/\/pueblo.lbl.gov\/~olken\/mendel\/sampling\/bibliography.htm.  Olken F. and Rotem D. 1993. Random sampling from databases: A survey. http:\/\/pueblo.lbl.gov\/~olken\/mendel\/sampling\/bibliography.htm."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539793255151"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1721837.1721859","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1721837.1721859","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:23:38Z","timestamp":1750249418000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1721837.1721859"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,3]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["10.1145\/1721837.1721859"],"URL":"https:\/\/doi.org\/10.1145\/1721837.1721859","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"type":"print","value":"1549-6325"},{"type":"electronic","value":"1549-6333"}],"subject":[],"published":{"date-parts":[[2010,3]]},"assertion":[{"value":"2004-09-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2009-10-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-04-06","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}