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Yangyang Xu, J. Cui (2012)
Multitask n-vehicle exploration problem: Complexity and algorithmJournal of Systems Science and Complexity, 25
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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.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jun 10, 2012
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