Abstract
We discuss a variant of the multi-task n-vehicle exploration problem. Instead of requiring an optimal permutation of vehicles in every group, the new problem requires all vehicles in a group to arrive at the same destination. Given n tasks with assigned consume-time and profit, it may also be viewed as a maximization of every processor’s average profit. Further, we propose a new kind of partition problem in fractional form and analyze its computational complexity. By regarding fractional partition as a special case, we prove that the average profit maximization problem is NP-hard when the number of processors is fixed and it is strongly NPhard in general. At last, a pseudo-polynomial time algorithm for the average profit maximization problem and the fractional partition problem is presented, using the idea of the pseudo-polynomial time algorithm for the classical partition problem.
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Supported by Daqing oilfield company Project of PetroCHINA under Grant (dqc-2010-xdgl-ky-002), Key Laboratory of Management, Decision and Information Systems, Chinese Academy of Sciences, and Beijing Research Center of Urban System Engineering.
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Xu, Yy., Cui, Jc. A variant of multi-task n-vehicle exploration problem: Maximizing every processor’s average profit. Acta Math. Appl. Sin. Engl. Ser. 28, 463–474 (2012). https://doi.org/10.1007/s10255-012-0162-6
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DOI: https://doi.org/10.1007/s10255-012-0162-6
Keywords
- multi-task n-vehicle exploration problem (MTNVEP)
- maximizing average profit (MAP)
- fractional partition (FP)
- NP-complete
- strongly NP-complete