{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:14:04Z","timestamp":1750306444129,"version":"3.41.0"},"reference-count":15,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T00:00:00Z","timestamp":1441670400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"German Research Foundation (DFG) within the Collaborative Research Center On-The-Fly Computing"},{"name":"Graduate School on Applied Network Science"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Parallel Comput."],"published-print":{"date-parts":[[2015,11,2]]},"abstract":"<jats:p>We present a new online algorithm for profit-oriented scheduling on multiple speed-scalable processors and provide a tight analysis of the algorithm\u2019s competitiveness. Our results generalize and improve upon work by Chan et al. [2010], which considers a single speed-scalable processor. Using significantly different techniques, we can not only extend their model to multiprocessors but also prove an enhanced and tight competitive ratio for our algorithm.<\/jats:p>\n          <jats:p>\n            In our scheduling problem, jobs arrive over time and are preemptable. They have different workloads, values, and deadlines. The scheduler may decide not to finish a job but instead to suffer a loss equaling the job\u2019s value. However, to process a job\u2019s workload until its deadline the scheduler must invest a certain amount of energy. The cost of a schedule is the sum of lost values and invested energy. In order to finish a job, the scheduler has to determine which processors to use and set their speeds accordingly. A processor\u2019s energy consumption is power P\n            <jats:sub>\u03b1<\/jats:sub>\n            (\n            <jats:italic>s<\/jats:italic>\n            ) integrated over time, where P\n            <jats:sub>\u03b1<\/jats:sub>\n            (\n            <jats:italic>s<\/jats:italic>\n            )=\n            <jats:italic>s<\/jats:italic>\n            <jats:sup>\u03b1<\/jats:sup>\n            is the power consumption when running at speed\n            <jats:italic>s<\/jats:italic>\n            . Since we consider the online variant of the problem, the scheduler has no knowledge about future jobs. This problem was introduced by Chan et al. [2010] for the case of a single processor. They presented an online algorithm that is \u03b1\n            <jats:sup>\u03b1<\/jats:sup>\n            + 2\n            <jats:italic>e<\/jats:italic>\n            \u03b1-competitive. We provide an online algorithm for the case of multiple processors with an improved competitive ratio of \u03b1\n            <jats:sup>\u03b1<\/jats:sup>\n            .\n          <\/jats:p>","DOI":"10.1145\/2809872","type":"journal-article","created":{"date-parts":[[2015,9,15]],"date-time":"2015-09-15T12:09:15Z","timestamp":1442318955000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Profitable Scheduling on Multiple Speed-Scalable Processors"],"prefix":"10.1145","volume":"2","author":[{"given":"Peter","family":"Kling","sequence":"first","affiliation":[{"name":"University of Paderborn, Heinz Nixdorf Institute"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Pietrzyk","sequence":"additional","affiliation":[{"name":"University of Paderborn, Heinz Nixdorf Institute, Paderborn, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,9,8]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.4230\/LIPIcs.STACS.2011.1"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1989493.1989539"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-02927-1_14"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2004.24"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1206035.1206038"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/MC.2007.443"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISPA.2008.128"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.5555\/993483"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1561\/0400000024"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18318-8_6"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/EMRTS.2004.1311011"},{"key":"e_1_2_1_12_1","volume-title":"Proceedings of the 10th Workshop on Approximation and Online Algorithms (WAOA).","author":"Gupta Anupam","year":"2012","unstructured":"Anupam Gupta, Ravishankar Krishnaswamy, and Kirk Pruhs. 2012. Online primal-dual for non-linear optimization with applications to speed scaling. In Proceedings of the 10th Workshop on Approximation and Online Algorithms (WAOA)."},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/2486159.2486183"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-15369-3_27"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.5555\/795662.796264"}],"container-title":["ACM Transactions on Parallel Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2809872","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2809872","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T05:42:54Z","timestamp":1750225374000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2809872"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,8]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,11,2]]}},"alternative-id":["10.1145\/2809872"],"URL":"https:\/\/doi.org\/10.1145\/2809872","relation":{},"ISSN":["2329-4949","2329-4957"],"issn-type":[{"type":"print","value":"2329-4949"},{"type":"electronic","value":"2329-4957"}],"subject":[],"published":{"date-parts":[[2015,9,8]]},"assertion":[{"value":"2013-10-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-06-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-09-08","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}