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Algorithms"],"published-print":{"date-parts":[[2012,4]]},"abstract":"<jats:p>\n            We propose and study a new class of online problems, which we call\n            <jats:italic>online tracking<\/jats:italic>\n            . Suppose an observer, say Alice, observes a multivalued function\n            <jats:italic>f<\/jats:italic>\n            : Z\n            <jats:sup>+<\/jats:sup>\n            \u2192 Z\n            <jats:italic>\n              <jats:sup>d<\/jats:sup>\n            <\/jats:italic>\n            over time in an online fashion, that is, she only sees\n            <jats:italic>f<\/jats:italic>\n            (\n            <jats:italic>t<\/jats:italic>\n            ) for\n            <jats:italic>\n              t\u2264t\n              <jats:sub>now<\/jats:sub>\n            <\/jats:italic>\n            where\n            <jats:italic>\n              t\n              <jats:sub>now<\/jats:sub>\n            <\/jats:italic>\n            is the current time. She would like to keep a tracker, say Bob, informed of the current value of\n            <jats:italic>f<\/jats:italic>\n            at all times. Under this setting, Alice could send new values of\n            <jats:italic>f<\/jats:italic>\n            to Bob from time to time, so that the current value of\n            <jats:italic>f<\/jats:italic>\n            is always within a distance of \u0394 to the last value received by Bob. We give competitive online algorithms whose communication costs are compared with the optimal offline algorithm that knows the entire\n            <jats:italic>f<\/jats:italic>\n            in advance. We also consider variations of the problem where Alice is allowed to send predictions to Bob, to further reduce communication for well-behaved functions. These online tracking problems have a variety of application, ranging from sensor monitoring, location-based services, to publish\/subscribe systems.\n          <\/jats:p>","DOI":"10.1145\/2151171.2151175","type":"journal-article","created":{"date-parts":[[2012,4,24]],"date-time":"2012-04-24T18:41:10Z","timestamp":1335292870000},"page":"1-16","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Multidimensional online tracking"],"prefix":"10.1145","volume":"8","author":[{"given":"Ke","family":"Yi","sequence":"first","affiliation":[{"name":"Hong Kong University of Science and Technology, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Hong Kong University of Science and Technology, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2012,4,25]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1545"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/MPRV.2003.1186725"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/1008731.1008733"},{"key":"e_1_2_1_4_1","volume-title":"Proceedings of the International Conference on Very Large Databases.","author":"Chandramouli B.","unstructured":"Chandramouli , B. , Phillips , J. 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