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ACM"],"published-print":{"date-parts":[[2012,8]]},"abstract":"<jats:p>\n            We study the weighted version of the classic online paging problem where there is a weight (cost) for fetching each page into the cache. We design a randomized\n            <jats:italic>O<\/jats:italic>\n            (log\n            <jats:italic>k<\/jats:italic>\n            )-competitive online algorithm for this problem, where\n            <jats:italic>k<\/jats:italic>\n            is the cache size. This is the first randomized\n            <jats:italic>o<\/jats:italic>\n            (\n            <jats:italic>k<\/jats:italic>\n            )-competitive algorithm and its competitive ratio matches the known lower bound for the problem, up to constant factors. More generally, we design an\n            <jats:italic>O<\/jats:italic>\n            (log(\n            <jats:italic>k<\/jats:italic>\n            \/(\n            <jats:italic>k<\/jats:italic>\n            \u2212\n            <jats:italic>h<\/jats:italic>\n            + 1)))-competitive online algorithm for the version of the problem where the online algorithm has cache size\n            <jats:italic>k<\/jats:italic>\n            and it is compared to an optimal offline solution with cache size\n            <jats:italic>h<\/jats:italic>\n            \u2264\n            <jats:italic>k<\/jats:italic>\n            .\n          <\/jats:p>\n          <jats:p>\n            Our solution is based on a two-step approach. We first obtain an\n            <jats:italic>O<\/jats:italic>\n            (log\n            <jats:italic>k<\/jats:italic>\n            )-competitive fractional algorithm based on an online primal-dual approach. Next, we obtain a randomized algorithm by rounding in an online manner the fractional solution to a probability distribution on the possible cache states. We also give an online primal-dual randomized\n            <jats:italic>O<\/jats:italic>\n            (log\n            <jats:italic>N<\/jats:italic>\n            )-competitive algorithm for the Metrical Task System problem (MTS) on a weighted star metric on\n            <jats:italic>N<\/jats:italic>\n            leaves.\n          <\/jats:p>","DOI":"10.1145\/2339123.2339126","type":"journal-article","created":{"date-parts":[[2012,9,4]],"date-time":"2012-09-04T12:50:47Z","timestamp":1346763047000},"page":"1-24","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":45,"title":["A Primal-Dual Randomized Algorithm for Weighted Paging"],"prefix":"10.1145","volume":"59","author":[{"given":"Nikhil","family":"Bansal","sequence":"first","affiliation":[{"name":"Eindhoven University of Technology"}]},{"given":"Niv","family":"Buchbinder","sequence":"additional","affiliation":[{"name":"Open University of Israel"}]},{"given":"Joseph (Seffi)","family":"Naor","sequence":"additional","affiliation":[{"name":"Technion"}]}],"member":"320","published-online":{"date-parts":[[2012,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(98)00116-9"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","unstructured":"Adamaszek A. Czumaj A. Englert M. and R\u00e4cke H. 2012. An O(log k)-competitive algorithm for generalized caching. In SODA. 1681--1689. Adamaszek A. Czumaj A. Englert M. and R\u00e4cke H. 2012. An O (log k )-competitive algorithm for generalized caching. In SODA . 1681--1689.","DOI":"10.1137\/1.9781611973099.133"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-003-0436-0"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2011.63"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1374376.1374412"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/502102.502107"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/258533.258667"},{"key":"e_1_2_1_8_1","unstructured":"Blum A. Furst M. and Tomkins A. 1996. What to do with your free time: Algorithms for infrequent requests and randomized weighted caching. Manuscript. (www.cs.cmu.edu) Blum A. Furst M. and Tomkins A. 1996. What to do with your free time: Algorithms for infrequent requests and randomized weighted caching. Manuscript. (www.cs.cmu.edu)"},{"volume-title":"Online computation and competitive analysis","author":"Borodin A.","key":"e_1_2_1_9_1","unstructured":"Borodin , A. and El-Yaniv , R. 1998. Online computation and competitive analysis . Cambridge University Press . Borodin, A. and El-Yaniv, R. 1998. Online computation and competitive analysis. Cambridge University Press."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/146585.146588"},{"volume-title":"Proceedings of the 15th Annual European Symposium. 253--264","author":"Buchbinder N.","key":"e_1_2_1_11_1","unstructured":"Buchbinder , N. , Jain , K. , and Naor , J. S . 2007. Online primal-dual algorithms for maximizing ad-auctions revenue . In Proceedings of the 15th Annual European Symposium. 253--264 . Buchbinder, N., Jain, K., and Naor, J. S. 2007. Online primal-dual algorithms for maximizing ad-auctions revenue. In Proceedings of the 15th Annual European Symposium. 253--264."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/11561071_61"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1148109.1148159"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1561\/0400000024"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/0404017"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/0220008"},{"volume-title":"Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms. 879--880","author":"Cohen E.","key":"e_1_2_1_17_1","unstructured":"Cohen , E. and Kaplan , H . 1999. LP-based analysis of greedy-dual-size . In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms. 879--880 . Cohen, E. and Kaplan, H. 1999. LP-based analysis of greedy-dual-size. In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms. 879--880."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/1374376.1374411"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(91)90041-V"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539700376159"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(05)80060-1"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/258533.258666"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-001-0095-6"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/210118.210128"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(90)90003-W"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01759073"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/2786.2793"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.5555\/127787.127832"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01189992"}],"container-title":["Journal of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2339123.2339126","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2339123.2339126","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T09:21:08Z","timestamp":1750238468000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2339123.2339126"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,8]]},"references-count":29,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["10.1145\/2339123.2339126"],"URL":"https:\/\/doi.org\/10.1145\/2339123.2339126","relation":{},"ISSN":["0004-5411","1557-735X"],"issn-type":[{"type":"print","value":"0004-5411"},{"type":"electronic","value":"1557-735X"}],"subject":[],"published":{"date-parts":[[2012,8]]},"assertion":[{"value":"2009-09-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-05-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-08-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}