Abstract
This paper extends the single-task n-Vehicle Exploration Problem to Multitask n-Vehicle Exploration Problem (MTNVEP), by combining n-Vehicle Exploration Problem with Job Scheduling Problem. At first, the authors prove that MTNVEP is NP-hard for fixed number of tasks, and it is strongly NP-hard for general number of tasks. Then they propose an improved accurate algorithm with computing time O(n3n), which is better than O(n!) as n becomes sufficiently large. Moreover, four heuristic algorithms are proposed. Effectiveness of the heuristic algorithms is illustrated by experiments at last.
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References
R. Yang, A traffic problem with oil and its extension, Mathematical Communication, 1999, 9: 44–45 (in Chinese).
X. Y. Li and J. C. Cui, Efficient algorithm for a kind of exploration problem with n vehicles, Journal of System Engineering, 2008, 8: 444–448.
X. Xia and J. C. Cui, A method of estimating computational complexity based on input conditions for n-vehicle problem, Acta Mathematicae Applicatae Sinica (English Series), 2010, 26(1): 1–12.
L. L. Liang, A problem of permutation optimization, Journal of Guangxi University for Nationalities, 2006, 12(4): 72–76 (in Chinese).
P. Chretienne, E. G. Coffman, J. K. Lenstra, and L. Zhen, Scheduling Theory and Its Applications, John Wiley & Sons, Chichester, 1995.
M. Russell, Graph Theory, John Wiley & Sons, New York, 2001.
G. Gutin and A. P. Punnen, The Traveling Salesman Problem and Its Variations, Kluwer, Netherlands, 2002.
P. Brucker, Scheduling Algorithm, Springer, Berlin, 1998.
N. Andelman, F. Michal, and M. Yishay, Strong price of anarchy, Games and Economic Behavior, 2009, 65(2): 289–317.
F. Michal and T. Tami, Approximate strong equilibrium in Job Scheduling Games, Proceedings of the 1st International Symposium on Algorithmic Game Theory (ed. by B. Monien and U. P. Schroeder), Paderborn, 2008.
I. Wegener, Complexity Theory, Science Press, Beijing, 2006.
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NPCompleteness, W. H. Freeman, New York, 1979.
R. Karp, Reducibility among combinatorial problems, Complexity of Computer Computations: The Proceedings of a Symposium on the Complexity of Computer Computations, (ed. by R. E. Miller and J. Thatcher), Plenum, New York, 1972.
B. Hayes, The easiest hard problem, American Scientist, 2002, 90(2): 113–117.
S. Mertens, The easiest hard problem: Number partitioning, Computational Complexity and Statistical Physics, 2006, 125(2): 125–140.
M. R. Garey and D. S. Johnson, Complexity results for multiprocessor scheduling under resource constraints, SIAM J. Computing, 1975, 4(4): 397–411.
J. Kleinberg and E. Tardos, Algorithm Design, Addison Wesley, United States Edition, 2005, 3.
D. S. Hochbaum, Approximation Algorithm for NP-Hard Problem, PWS Publishing Company, Boston, 1997.
V. A. Zorich, Mathematical Analysis I, Springer, Berlin, 2004.
C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall Inc, 1982.
D. Z. Du, K. Ko, and J. Wang, Introduction to Computational Complexity, Higher Education Press, 2002.
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This research was partly supported by Daqing Oilfield Company Project of PetroCHINA under Grant No. dqc-2010-xdgl-ky-002 and Key Laboratory of Management, Decision and Information Systems, Chinese Academy of Sciences.
This paper was recommended for publication by Editor Hanqin ZHANG.
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Xu, Y., Cui, J. Multitask n-vehicle exploration problem: Complexity and algorithm. J Syst Sci Complex 25, 1080–1092 (2012). https://doi.org/10.1007/s11424-012-9324-0
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DOI: https://doi.org/10.1007/s11424-012-9324-0