{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:14:42Z","timestamp":1750306482067,"version":"3.41.0"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2016,2,8]],"date-time":"2016-02-08T00:00:00Z","timestamp":1454889600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"National Science Foundation","award":["CCF 0832797"],"award-info":[{"award-number":["CCF 0832797"]}]},{"name":"Gordon Wu fellowship"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2016,2,8]]},"abstract":"<jats:p>\n            In this article, we show how to compute the width of a dynamic set of low-dimensional points in the streaming model. In particular, we assume that the stream contains both insertions of points and deletions of points to a set\n            <jats:italic>S<\/jats:italic>\n            , and the goal is to compute the width of the set\n            <jats:italic>S<\/jats:italic>\n            , namely the minimal distance between two parallel hyperplanes sandwiching the point set\n            <jats:italic>S<\/jats:italic>\n            .\n          <\/jats:p>\n          <jats:p>\n            Our algorithm (1 + \u03f5) approximates the width of the set\n            <jats:italic>S<\/jats:italic>\n            using space polylogarithmic in the size of\n            <jats:italic>S<\/jats:italic>\n            and the aspect ratio of\n            <jats:italic>S<\/jats:italic>\n            . This is the first such algorithm that supports both insertions and deletions of points to the set\n            <jats:italic>S<\/jats:italic>\n            : previous algorithms for approximating the width of a point set only supported additions [Agarwal et al. 2004; Chan 2006], or a sliding window [Chan and Sadjad 2006].\n          <\/jats:p>\n          <jats:p>This solves an open question from the \u201c2009 Kanpur list\u201d of open problems in data streams, property testing, and related topics [Indyk et al. 2011].<\/jats:p>","DOI":"10.1145\/2847259","type":"journal-article","created":{"date-parts":[[2016,2,8]],"date-time":"2016-02-08T22:37:07Z","timestamp":1454971027000},"page":"1-10","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Width of Points in the Streaming Model"],"prefix":"10.1145","volume":"12","author":[{"given":"Alexandr","family":"Andoni","sequence":"first","affiliation":[{"name":"Microsoft Research"}]},{"given":"Huy L.","family":"Nguy\u00ea\u0771n","sequence":"additional","affiliation":[{"name":"Princeton University"}]}],"member":"320","published-online":{"date-parts":[[2016,2,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1008731.1008736"},{"key":"e_1_2_1_2_1","volume-title":"Varadarajan","author":"Agarwal Pankaj K.","year":"2005","unstructured":"Pankaj K. Agarwal , Sariel Har-Peled , and Kasturi R . Varadarajan . 2005 . Geometric approximation via coresets\u2014survey. In Combinatorial and Computational Geometry. University Press . Pankaj K. Agarwal, Sariel Har-Peled, and Kasturi R. Varadarajan. 2005. Geometric approximation via coresets\u2014survey. In Combinatorial and Computational Geometry. University Press."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/235809.235813"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2005.10.002"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00454-009-9165-3"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195906001975"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-004-1105-2"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1064092.1064116"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1060590.1060622"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1007352.1007413"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-27836-8_66"},{"key":"e_1_2_1_12_1","volume-title":"Open problems in data streams, property testing, and related topics. Retrieved","author":"Indyk Piotr","year":"2015","unstructured":"Piotr Indyk , Andrew McGregor , Ilan Newman , and Krzysztof Onak . 2011. Open problems in data streams, property testing, and related topics. Retrieved December 8, 2015 , from http:\/\/www.cs.umass.edu\/mcgregor\/papers\/11-openproblems.pdf. Piotr Indyk, Andrew McGregor, Ilan Newman, and Krzysztof Onak. 2011. Open problems in data streams, property testing, and related topics. Retrieved December 8, 2015, from http:\/\/www.cs.umass.edu\/mcgregor\/papers\/11-openproblems.pdf."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1561\/9781933019604"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.5555\/2095116.2095221"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2847259","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2847259","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T05:48:23Z","timestamp":1750225703000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2847259"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,8]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,2,8]]}},"alternative-id":["10.1145\/2847259"],"URL":"https:\/\/doi.org\/10.1145\/2847259","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"type":"print","value":"1549-6325"},{"type":"electronic","value":"1549-6333"}],"subject":[],"published":{"date-parts":[[2016,2,8]]},"assertion":[{"value":"2012-06-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-12-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-02-08","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}