{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T22:06:18Z","timestamp":1775253978764,"version":"3.50.1"},"reference-count":28,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2007,11,1]],"date-time":"2007-11-01T00:00:00Z","timestamp":1193875200000},"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":[[2007,11]]},"abstract":"<jats:p>\n            We consider the problem of minimizing the total weighted flow time on a single machine with preemptions. We give an online algorithm that is\n            <jats:italic>O<\/jats:italic>\n            (\n            <jats:italic>k<\/jats:italic>\n            )-competitive for\n            <jats:italic>k<\/jats:italic>\n            weight classes. This implies an\n            <jats:italic>O<\/jats:italic>\n            (log\n            <jats:italic>W<\/jats:italic>\n            )-competitive algorithm, where\n            <jats:italic>W<\/jats:italic>\n            is the maximum to minimum ratio of weights. This algorithm also implies an\n            <jats:italic>O<\/jats:italic>\n            (log\n            <jats:italic>n<\/jats:italic>\n            + log\n            <jats:italic>P<\/jats:italic>\n            )-approximation ratio for the problem, where\n            <jats:italic>P<\/jats:italic>\n            is the ratio of the maximum to minimum job size and\n            <jats:italic>n<\/jats:italic>\n            is the number of jobs. We also consider the nonclairvoyant setting where the size of a job is unknown upon its arrival and becomes known to the scheduler only when the job meets its service requirement. We consider the resource augmentation model, and give a (1 + \u03b5)-speed, (1 +1\/\u03b5)-competitive online algorithm.\n          <\/jats:p>","DOI":"10.1145\/1290672.1290676","type":"journal-article","created":{"date-parts":[[2007,11,30]],"date-time":"2007-11-30T14:24:58Z","timestamp":1196432698000},"page":"39","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":31,"title":["Minimizing weighted flow time"],"prefix":"10.1145","volume":"3","author":[{"given":"Nikhil","family":"Bansal","sequence":"first","affiliation":[{"name":"IBM T.J. Watson Research, Yorktown, NY"}]},{"given":"Kedar","family":"Dhamdhere","sequence":"additional","affiliation":[{"name":"Google Inc., Mountain View, CA"}]}],"member":"320","published-online":{"date-parts":[[2007,11]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), 32--43","author":"Afrati F.","unstructured":"Afrati , F. , Bampis , E. , Chekuri , C. , Karger , D. , Kenyon , C. , Khanna , S. , Millis , I. , Queyranne , M. , Skutella , M. , Stein , C. , and Sviridenko , M . 1999. Approximation schemes for minimizing average weighted completion time with release dates . In Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), 32--43 . Afrati, F., Bampis, E., Chekuri, C., Karger, D., Kenyon, C., Khanna, S., Millis, I., Queyranne, M., Skutella, M., Stein, C., and Sviridenko, M. 1999. Approximation schemes for minimizing average weighted completion time with release dates. In Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), 32--43."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/777412.777415"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/301250.301304"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2004.07.008"},{"key":"e_1_2_1_5_1","volume-title":"Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS), 260--270","author":"Bansal N.","unstructured":"Bansal , N. , Dhamdhere , K. , Konemann , J. , and Sinha , A . 2003. Non-Clairvoyant scheduling for minimizing mean slowdown . In Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS), 260--270 . Bansal, N., Dhamdhere, K., Konemann, J., and Sinha, A. 2003. Non-Clairvoyant scheduling for minimizing mean slowdown. In Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS), 260--270."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/780542.780580"},{"key":"e_1_2_1_7_1","volume-title":"Proceedings of the Latin American Symposium on Theoretical Informatics (LATIN), 434--443","author":"Bansal N.","unstructured":"Bansal , N. , and Pruhs , K . 2004. Server scheduling in the weighted &ell;<sub>p<\/sub> norm . In Proceedings of the Latin American Symposium on Theoretical Informatics (LATIN), 434--443 . Bansal, N., and Pruhs, K. 2004. Server scheduling in the weighted &ell;<sub>p<\/sub> norm. In Proceedings of the Latin American Symposium on Theoretical Informatics (LATIN), 434--443."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/1008731.1008732"},{"key":"e_1_2_1_9_1","volume-title":"Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 548--557","author":"Becchetti L.","unstructured":"Becchetti , L. , Leonardi , S. , and Muthukrishnan , S . 2000. Scheduling to minimize average stretch without migration . In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 548--557 . Becchetti, L., Leonardi, S., and Muthukrishnan, S. 2000. Scheduling to minimize average stretch without migration. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 548--557."},{"key":"e_1_2_1_10_1","volume-title":"Proceedings of the International Workshop on Randomination and Approximation Techniques (RANDOM-APPROX), 36--47","author":"Becchetti L.","unstructured":"Becchetti , L. , Leonardi , S. , Spaccamela , A. M. , and Pruhs , K . 2001. Online weighted flow time and deadline scheduling . In Proceedings of the International Workshop on Randomination and Approximation Techniques (RANDOM-APPROX), 36--47 . Becchetti, L., Leonardi, S., Spaccamela, A. M., and Pruhs, K. 2001. Online weighted flow time and deadline scheduling. In Proceedings of the International Workshop on Randomination and Approximation Techniques (RANDOM-APPROX), 36--47."},{"key":"e_1_2_1_11_1","volume-title":"Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 270--279","author":"Bender M.","unstructured":"Bender , M. , Chakrabarti , S. , and Muthukrishnan , S . 1998. Flow and stretch metrics for scheduling continuous job streams . In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 270--279 . Bender, M., Chakrabarti, S., and Muthukrishnan, S. 1998. Flow and stretch metrics for scheduling continuous job streams. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 270--279."},{"key":"e_1_2_1_12_1","volume-title":"Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA).","author":"Bender M.","unstructured":"Bender , M. , Muthukrishnan , S. , and Rajaraman , R . 2002. Improved algorithms for stretch scheduling . In Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). Bender, M., Muthukrishnan, S., and Rajaraman, R. 2002. Improved algorithms for stretch scheduling. In Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1007352.1007411"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/509907.509954"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/380752.380778"},{"key":"e_1_2_1_16_1","volume-title":"Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 609-- 618","author":"Chekuri C.","unstructured":"Chekuri , C. , Motwani , R. , Natarajan , B. , and Stein , C . 1997. Approximation techniques for average completion time scheduling . In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 609-- 618 . Chekuri, C., Motwani, R., Natarajan, B., and Stein, C. 1997. Approximation techniques for average completion time scheduling. In Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (SODA), 609-- 618."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.5555\/2789945.2789946"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/347476.347479"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/792538.792545"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/237814.237989"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70743-X"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/258533.258562"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)90151-1"},{"key":"e_1_2_1_24_1","volume-title":"Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), 433--442","author":"Muthukrishnan S.","unstructured":"Muthukrishnan , S. , Rajaraman , R. , Shaheen , A. , and Gehrke , J . 1999. Online scheduling to minimize average stretch . In Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), 433--442 . Muthukrishnan, S., Rajaraman, R., Shaheen, A., and Gehrke, J. 1999. Online scheduling to minimize average stretch. In Proceedings of the IEEE Symposium on Foundations of Computer Science (FOCS), 433--442."},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/258533.258570"},{"key":"e_1_2_1_26_1","unstructured":"Pruhs K. Sgall J. and Torng E. 2004. Online scheduling. In Handbook of Scheduling: Algorithms Models and Performance Analysis. Ratan FL Chap. 35 CRC Press.  Pruhs K. Sgall J. and Torng E. 2004. Online scheduling. In Handbook of Scheduling: Algorithms Models and Performance Analysis. Ratan FL Chap. 35 CRC Press."},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.16.3.687"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800030106"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1290672.1290676","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1290672.1290676","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T14:52:24Z","timestamp":1750258344000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1290672.1290676"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11]]},"references-count":28,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,11]]}},"alternative-id":["10.1145\/1290672.1290676"],"URL":"https:\/\/doi.org\/10.1145\/1290672.1290676","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"value":"1549-6325","type":"print"},{"value":"1549-6333","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11]]},"assertion":[{"value":"2007-11-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}