{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:40:33Z","timestamp":1759848033950},"reference-count":12,"publisher":"Association for Computing Machinery (ACM)","issue":"2","content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Algorithms"],"published-print":{"date-parts":[[2006,4]]},"abstract":"<jats:p>\n            We consider the problem of scheduling a set of\n            <jats:italic>n<\/jats:italic>\n            unit-execution-time (UET) tasks, with precedence constraints, on\n            <jats:italic>m<\/jats:italic>\n            \u2265 1 parallel and identical processors so as to minimize the mean flow time. For two processors, the Coffman--Graham algorithm gives a schedule that simultaneously minimizes the mean flow time and the makespan. The problem becomes strongly NP-hard for an arbitrary number of processors, although the complexity is not known for each fixed\n            <jats:italic>m<\/jats:italic>\n            \u2265 3. For arbitrary precedence constraints, we show that the Coffman--Graham algorithm gives a schedule with a worst-case bound no more than 2, and we give examples showing that the bound is tight. For intrees, the problem can be solved in polynomial time for each fixed\n            <jats:italic>m<\/jats:italic>\n            \u2265 1, although the complexity is not known for an arbitrary number of processors. We show that Hu's algorithm (which is optimal for the makespan objective) yields a schedule with a worst-case bound no more than 1.5, and we give examples showing that the ratio can approach 1.308999.\n          <\/jats:p>","DOI":"10.1145\/1150334.1150340","type":"journal-article","created":{"date-parts":[[2006,10,18]],"date-time":"2006-10-18T18:11:32Z","timestamp":1161195092000},"page":"244-262","update-policy":"http:\/\/dx.doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Minimizing mean flow time for UET tasks"],"prefix":"10.1145","volume":"2","author":[{"given":"Yumei","family":"Huo","sequence":"first","affiliation":[{"name":"New Jersey Institute of Technology, Newark, NJ"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joseph Y.-T.","family":"Leung","sequence":"additional","affiliation":[{"name":"New Jersey Institute of Technology, Newark, NJ"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2006,4]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Baptiste Ph. Brucker P. Knust S. and Timkovsky V. G. 2002. Fourteen notes on equal-processing-time scheduling. OSM Reihe P Heft 246.  Baptiste Ph. Brucker P. Knust S. and Timkovsky V. G. 2002. Fourteen notes on equal-processing-time scheduling. OSM Reihe P Heft 246."},{"key":"e_1_2_1_2_1","first-page":"407","article-title":"A polynomial algorithm for P&verbar;pj &equals; 1, rj, outtree&verbar; &sum;Cj","volume":"56","author":"Brucker P.","year":"2003","journal-title":"Math. Meth. Oper. Res."},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1007\/BF00288685","article-title":"Optimal scheduling for two-processor systems","volume":"1","author":"Coffman E. G.","year":"1972","journal-title":"Acta Inf."},{"key":"e_1_2_1_4_1","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s00236-003-0119-6","article-title":"Ideal preemptive schedules on two processors","volume":"39","author":"Coffman E. G.","year":"2003","journal-title":"Acta Inf."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/0890-5401(91)90009-Q"},{"key":"e_1_2_1_6_1","unstructured":"Garey M. R. and Johnson D. S. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company San Francisco CA.   Garey M. R. and Johnson D. S. 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company San Francisco CA."},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/S0167-5060(08)70356-X","article-title":"Optimization and approximation in deterministic sequencing and scheduling: A survey","volume":"5","author":"Graham R. L.","year":"1979","journal-title":"Ann. Disc. Math."},{"key":"e_1_2_1_8_1","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1137\/0123021","article-title":"Single-machine job sequencing with treelike precedence ordering and linear delay penalties","volume":"23","author":"Horn W. A.","year":"1972","journal-title":"SIAM J. Appl. Math."},{"key":"e_1_2_1_9_1","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1287\/opre.9.6.841","article-title":"Parallel sequencing and assembly line problems","volume":"9","author":"Hu T. C.","year":"1961","journal-title":"Oper. Res."},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1137\/0206037","article-title":"Worst case analysis of two scheduling algorithms","volume":"6","author":"Lam S.","year":"1977","journal-title":"SIAM J. Comput."},{"key":"e_1_2_1_11_1","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/S0167-5060(08)70323-6","article-title":"Sequencing jobs to minimize total weighted completion time subject to precedence constraints","volume":"2","author":"Lawler E. L.","year":"1978","journal-title":"Ann. Disc. Math."},{"key":"e_1_2_1_12_1","first-page":"1","article-title":"Scheduling with deadlines and loss functions. Manage","volume":"6","author":"McNaughton R.","year":"1959","journal-title":"Sci."}],"container-title":["ACM Transactions on Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1150334.1150340","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T20:35:59Z","timestamp":1672259759000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1150334.1150340"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,4]]},"references-count":12,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,4]]}},"alternative-id":["10.1145\/1150334.1150340"],"URL":"https:\/\/doi.org\/10.1145\/1150334.1150340","relation":{},"ISSN":["1549-6325","1549-6333"],"issn-type":[{"value":"1549-6325","type":"print"},{"value":"1549-6333","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,4]]},"assertion":[{"value":"2006-04-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}