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Job shop scheduling with unit length tasks
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 3, pp. 329-342

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In this paper, we consider a class of scheduling problems that are among the fundamental optimization problems in operations research. More specifically, we deal with a particular version called job shop scheduling with unit length tasks. Using the results of Hromkovič, Mömke, Steinhöfel, and Widmayer presented in their work Job Shop Scheduling with Unit Length Tasks: Bounds and Algorithms, we analyze the problem setting for 2 jobs with an unequal number of tasks. We contribute a deterministic algorithm which achieves a vanishing delay in certain cases and a randomized algorithm with a competitive ratio tending to 1. Furthermore, we investigate the problem with 3 jobs and we construct a randomized online algorithm which also has a competitive ratio tending to 1.

DOI : 10.1051/ita/2011132
Classification : 68Q25
Keywords: online algorithms, competitive analysis, job shop scheduling 
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     author = {Akveld, Meike and Bernhard, Raphael},
     title = {Job shop scheduling with unit length tasks},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {329--342},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {3},
     year = {2012},
     doi = {10.1051/ita/2011132},
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     zbl = {1283.68158},
     language = {en},
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Akveld, Meike; Bernhard, Raphael. Job shop scheduling with unit length tasks. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 3, pp. 329-342. doi: 10.1051/ita/2011132

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