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On the On-Line k-Taxi Problem with Limited Look Ahead

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Combinatorial Optimization and Applications (COCOA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4616))

Abstract

Based on some new results concerning k-taxi problem, a new variant of the problem, namely the on-line k-taxi problem with limited look ahead (OTLLA) is proposed by our team. Compared with the traditional k-taxi problem, in which only the start and end points of the current service request are known at each step, the OTLLA has a basic realistic consideration: the start point of the first service request is given before the whole service sequence plays, and at each step the end of the current service request and the start point of the next service request are known. In this paper, after the formulation of the model of the OTLLA, some results concerning the competitive analysis for some special cases of OTLLA are given: the competitive algorithm so called Partial Greedy Algorithm (PGA) is designed and the competitive ratios are obtained. Furthermore, some comparisons between some on-line algorithms are developed. Finally, some conclusions are given and some future research directions are discussed.

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References

  1. Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communication of the ACM 28, 202–208 (1985)

    Article  MathSciNet  Google Scholar 

  2. Karlin, R., Manasse, M., Rudlph, L., Sleator, D.D.: Competitive snoopy caching. Algorithmica 3, 79–119 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  3. Manasse, M.S., McGeoch, L.A., Sleator, D.D.: Competitive algorithms for on-line problems. In: Proc. 20th Annual ACM Symp. on Theory of Computing, pp. 322–333. ACM Press, New York (1988)

    Google Scholar 

  4. Borodin, A., Linial, N., Sake, M.: An optimal on-line algorithm for metrical task systems. Journal of ACM 39, 745–763 (1992)

    Article  MATH  Google Scholar 

  5. Manasse, M.S., McGeoch, L.A., Sleator, D.D.: Competitive algorithms for server problems. Journal of Algorithms (11), 208–230 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ben-david, S., Borodin, A., Karp, R.M., ardos, G.T, Wigderson, A.: On the power if randomization in on-line algorithms. In: Proc. 22nd Annual ACM Symp. on Theory of Computing, pp. 379–386. ACM Press, New York (1990)

    Google Scholar 

  7. Woodall, D.R.: The bay restaurant- a linear storage problem. American Mathematical Monthly 81, 240–246 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kierstead, H.A., Trotter, W.T.: An extremal problem in recursive combinatorics. Congressus Numerantium 33, 143–153 (1981)

    MathSciNet  Google Scholar 

  9. Yao, A.C.C: New algorithm for bin packing. J. Assoc. Comput. Mach. 27, 207–227 (1980)

    MATH  MathSciNet  Google Scholar 

  10. Albers, S.: Online algorithms: a survey. Mathematical Programming 97(1-2), 3–26 (2003)

    MATH  MathSciNet  Google Scholar 

  11. Fiat, A., Woeginger, G.J.: Online algorithms: The state of the art. LNCS, vol. 1442. Springer, Heidelberg (1998)

    Google Scholar 

  12. Karp, R.: On-line algorithms versus offline algorithms: How Much is it Worth to Know the Future? In: Proc. IFIP 12th World Computer Congress, vol. 1, pp. 416–429 (1992)

    Google Scholar 

  13. Fleischer, R.: On the Bahncard Problem. In: Proc. TCS 2001, pp. 161–174 (2001)

    Google Scholar 

  14. Karlin, A.R., Kenyon, C., Randall, D.: Dynamic TCP Acknowledgement and Other Stories about e/(e − 1). In: Proc. STOC 2001, pp. 502–509 (2001)

    Google Scholar 

  15. Fujiwara, H., Iwama, K.: Average-case Competitive Analyses for Ski-rental Problems. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 476–488. Springer, Heidelberg (2002)

    Google Scholar 

  16. Xu, Y.F., Xu, W.J.: Competitive Algorithms for Online Leasing Problem in Probabilistic Environments. In: ISNN 2001, pp. 725–730 (2004)

    Google Scholar 

  17. Ma, W.M., Xu, Y.F., Wang, K.L.: On-line k-truck problem and its competitive algorithm. Journal of Global Optimization 21(1), 15–25 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  18. Ma, W.M., Xu, Y.F., You, J., Liu, J., Wang, K.L.: On the k-Truck Scheduling Problem. International Journal of Foundations of Computer Science 15(1), 127–141 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  19. Ma, W.M., You, J., Xu, Y.F., Liu, J., Wang, K.L.: On the on-line number of snacks problem. Journal of Global Optimization 24(4), 449–462 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  20. Ma, W.M., Liu, J., Chen, G.Q., You, J.: Competitive analysis for the on-line truck transportation problem. Journal of global optimization 34(4), 489–502 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  21. Xu, Y.F., Wang, K.L., Zhu, B.: On the k-taxi problem. Information 1, 2–4 (1999)

    MathSciNet  Google Scholar 

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Andreas Dress Yinfeng Xu Binhai Zhu

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© 2007 Springer-Verlag Berlin Heidelberg

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Ma, W., Gao, T., Wang, K. (2007). On the On-Line k-Taxi Problem with Limited Look Ahead. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_10

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  • DOI: https://doi.org/10.1007/978-3-540-73556-4_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73555-7

  • Online ISBN: 978-3-540-73556-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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