{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:15:18Z","timestamp":1750306518970,"version":"3.41.0"},"reference-count":15,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2015,1,13]],"date-time":"2015-01-13T00:00:00Z","timestamp":1421107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001711","name":"Swiss National Science Foundation","doi-asserted-by":"publisher","award":["200021-107880\/1"],"award-info":[{"award-number":["200021-107880\/1"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2015,1,13]]},"abstract":"<jats:p>\n            In this article, we consider a stochastic variant of the so-called\n            <jats:italic>Santa Claus<\/jats:italic>\n            problem. The Santa Claus problem is equivalent to the problem of scheduling a set of\n            <jats:italic>n<\/jats:italic>\n            jobs on\n            <jats:italic>m<\/jats:italic>\n            parallel machines without preemption, so as to\n            <jats:italic>maximize<\/jats:italic>\n            the\n            <jats:italic>minimum<\/jats:italic>\n            load. We consider the identical machine version of this scheduling problem with the additional restriction that the scheduler has only a\n            <jats:italic>guess<\/jats:italic>\n            of the processing times; that is, the processing time of a job is a\n            <jats:italic>random variable<\/jats:italic>\n            . We show that there is a critical value \u03c1 (\n            <jats:italic>n,m<\/jats:italic>\n            ) such that if the duration of the jobs is exponentially distributed and the expected values deviate by less than a multiplicative factor of \u03c1 (\n            <jats:italic>n,m<\/jats:italic>\n            ) from each other, then a greedy algorithm has an expected competitive ratio arbitrarily close to one; that is, it performs in expectation almost as good as an algorithm that knows the actual values\n            <jats:italic>in advance<\/jats:italic>\n            . On the other hand, if the expected values deviate by more than a multiplicative factor of \u03c1 (\n            <jats:italic>n,m<\/jats:italic>\n            ), then the expected performance is arbitrarily bad for\n            <jats:italic>all<\/jats:italic>\n            algorithms.\n          <\/jats:p>","DOI":"10.1145\/2651421","type":"journal-article","created":{"date-parts":[[2015,1,16]],"date-time":"2015-01-16T14:29:58Z","timestamp":1421418598000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Maximizing the Minimum Load for Random Processing Times"],"prefix":"10.1145","volume":"11","author":[{"given":"Stefanie","family":"Gerke","sequence":"first","affiliation":[{"name":"Royal Holloway University of London, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Konstantinos","family":"Panagiotou","sequence":"additional","affiliation":[{"name":"University of Munich, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Justus","family":"Schwartz","sequence":"additional","affiliation":[{"name":"ETH Zurich, Zurich, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Angelika","family":"Steger","sequence":"additional","affiliation":[{"name":"ETH Zurich, Zurich, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,1,13]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_1_1_1","DOI":"10.1145\/2229163.2229168"},{"doi-asserted-by":"publisher","key":"e_1_2_1_2_1","DOI":"10.1002\/(SICI)1099-1425(199808)1:2<67::AID-JOS6>3.0.CO;2-Y"},{"doi-asserted-by":"publisher","key":"e_1_2_1_3_1","DOI":"10.1145\/1132516.1132522"},{"doi-asserted-by":"publisher","key":"e_1_2_1_4_1","DOI":"10.1145\/1120680.1120683"},{"doi-asserted-by":"publisher","key":"e_1_2_1_5_1","DOI":"10.1287\/opre.33.3.548"},{"doi-asserted-by":"publisher","key":"e_1_2_1_6_1","DOI":"10.1016\/0167-6377(92)90004-M"},{"doi-asserted-by":"publisher","key":"e_1_2_1_7_1","DOI":"10.1137\/0603019"},{"unstructured":"M. R. Garey and D. S. Johnson. 1979. Computers and Intractability. W. H. Freeman and Co. San Francisco California. x &plus; 338 pages. A Guide to the Theory of NP-Completeness A Series of Books in Mathematical Sciences.   M. R. Garey and D. S. Johnson. 1979. Computers and Intractability. W. H. Freeman and Co. San Francisco California. x &plus; 338 pages. A Guide to the Theory of NP-Completeness A Series of Books in Mathematical Sciences.","key":"e_1_2_1_8_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_10_1","DOI":"10.1017\/S0305004100034241"},{"doi-asserted-by":"publisher","key":"e_1_2_1_11_1","DOI":"10.1080\/07408170490247340"},{"volume-title":"Probabilistic Methods for Algorithmic Discrete Mathematics. Algorithms Combin.","author":"McDiarmid C.","unstructured":"C. McDiarmid . 1998. Concentration . In Probabilistic Methods for Algorithmic Discrete Mathematics. Algorithms Combin. , Vol. 16 . Springer , Berlin , 195--248. C. McDiarmid. 1998. Concentration. In Probabilistic Methods for Algorithmic Discrete Mathematics. Algorithms Combin., Vol. 16. Springer, Berlin, 195--248.","key":"e_1_2_1_12_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_13_1","DOI":"10.1145\/1120582.1120585"},{"doi-asserted-by":"publisher","key":"e_1_2_1_14_1","DOI":"10.1007\/s00224-005-1261-z"},{"doi-asserted-by":"publisher","key":"e_1_2_1_15_1","DOI":"10.1016\/j.ic.2004.10.002"},{"doi-asserted-by":"publisher","key":"e_1_2_1_16_1","DOI":"10.1016\/S0167-6377(96)00055-7"}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2651421","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2651421","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:11:54Z","timestamp":1750227114000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2651421"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,13]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,1,13]]}},"alternative-id":["10.1145\/2651421"],"URL":"https:\/\/doi.org\/10.1145\/2651421","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"type":"print","value":"1549-6325"},{"type":"electronic","value":"1549-6333"}],"subject":[],"published":{"date-parts":[[2015,1,13]]},"assertion":[{"value":"2008-10-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2014-07-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-01-13","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}