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Hurink, J.L. and Paulus, J.J. (2007) Special cases of online parallel job scheduling. Beta Working Paper WP-235 Beta Research School for Operations Management and Logistics, Eindhoven. ISSN 1386-9213
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In this paper we consider the online scheduling of jobs, which require processing on a number of machines simultaneously. These jobs are presented to a decision maker one by one, where the next job becomes known as soon as the current job is scheduled. The objective is to minimize the makespan. For the problem with three machines we give a 2.8-competitive algorithm, improving upon the 3-competitive greedy algorithm. For the special case with arbitrary number of machines, where the jobs appear in non-increasing order of machine requirement, we give a 2.4815-competitive algorithm, improving the 2.75-competitive greedy algorithm.
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