{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:16:25Z","timestamp":1759637785187,"version":"3.41.0"},"reference-count":8,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2010,11,1]],"date-time":"2010-11-01T00:00:00Z","timestamp":1288569600000},"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":[[2010,11]]},"abstract":"<jats:p>\n            We continue the study of the online unit clustering problem, introduced by Chan and Zarrabi-Zadeh (\n            <jats:italic>Workshop on Approximation and Online Algorithms 2006<\/jats:italic>\n            , LNCS 4368, p. 121--131. Springer, 2006). We design a deterministic algorithm with a competitive ratio of 7\/4 for the one-dimensional case. This is the first deterministic algorithm that beats the bound of 2. It also has a better competitive ratio than the previous randomized algorithms. Moreover, we provide the first non-trivial deterministic lower bound, improve the randomized lower bound, and prove the first lower bounds for higher dimensions.\n          <\/jats:p>","DOI":"10.1145\/1868237.1868245","type":"journal-article","created":{"date-parts":[[2010,12,14]],"date-time":"2010-12-14T16:00:46Z","timestamp":1292342446000},"page":"1-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":15,"title":["On the online unit clustering problem"],"prefix":"10.1145","volume":"7","author":[{"given":"Leah","family":"Epstein","sequence":"first","affiliation":[{"name":"University of Haifa, Israel"}]},{"given":"Rob Van","family":"Stee","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Informatics, Germany"}]}],"member":"320","published-online":{"date-parts":[[2010,12,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/11970125_10"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539702418498"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190120212"},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","unstructured":"Kierstead H. A. 1998. Coloring graphs on-line. In Online Algorithms: The State of the Art A. Fiat and G. J. Woeginger Eds. Springer 281--305.   Kierstead H. A. 1998. Coloring graphs on-line. In Online Algorithms: The State of the Art A. Fiat and G. J. Woeginger Eds. Springer 281--305.","DOI":"10.1007\/BFb0029574"},{"key":"e_1_2_1_5_1","first-page":"143","article-title":"An extremal problem in recursive combinatorics","volume":"33","author":"Kierstead H. A.","year":"1981","unstructured":"Kierstead , H. A. , and Trotter , W. T. 1981 . An extremal problem in recursive combinatorics . Congr. Numer. 33 , 143 -- 153 . Kierstead, H. A., and Trotter, W. T. 1981. An extremal problem in recursive combinatorics. Congr. Numer. 33, 143--153.","journal-title":"Congr. Numer."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(89)90096-4"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1977.24"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.5555\/2394650.2394688"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1868237.1868245","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1868237.1868245","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:08:52Z","timestamp":1750248532000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1868237.1868245"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,11]]}},"alternative-id":["10.1145\/1868237.1868245"],"URL":"https:\/\/doi.org\/10.1145\/1868237.1868245","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"type":"print","value":"1549-6325"},{"type":"electronic","value":"1549-6333"}],"subject":[],"published":{"date-parts":[[2010,11]]},"assertion":[{"value":"2008-02-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2008-06-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-12-08","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}