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A variant of multi-task n-vehicle exploration problem: Maximizing every processor’s average profit

A variant of multi-task n-vehicle exploration problem: Maximizing every processor’s average profit 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A variant of multi-task n-vehicle exploration problem: Maximizing every processor’s average profit

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References (15)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Math Applications in Computer Science
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0162-6
Publisher site
See Article on Publisher Site

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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jun 10, 2012

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