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On-line Scheduling with a Monotonous Subsequence Constraint

  • Kelin LuoEmail author
  • Yinfeng Xu
  • Huili Zhang
  • Wei Luo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10336)

Abstract

In this paper, we study a new on-line scheduling problem that each server has to process a monotonous request subsequence. The customer requests are released over-list, and the operator has to decide whether or not to accept the current request and arrange it to a server immediately. The goal of this paper is to find a strategy which accepts the maximal requests. When the number of servers k is less than that of the request types m, we give several lower bounds for this problem. Also, we present the optimal strategy for \( k=1 \) and \( k=2 \) respectively.

Keywords

Scheduling On-line algorithm Competitive analysis Monotonous subsequence 

Notes

Acknowledgement

This work was partially supported by the NSFC (Grant No. 71601152), and by the China Postdoctoral Science Foundation (Grant No. 2016M592811).

References

  1. 1.
    Zervas, G., Proserpio, D., Byers, J.: The rise of the sharing economy: estimating the impact of Airbnb on the hotel industry. 18 November 2016. Boston U. School of Management Research Paper No. 2013–2016Google Scholar
  2. 2.
    Fredman, M.L.: On computing the length of longest increasing subsequences. Discret. Math. 11(1), 29–35 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Deorowicz, S.: An algorithm for solving the longest increasing circular subsequence problem. Inf. Process. Lett. 109(12), 630–634 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Romik, D.: The Surprising Mathematics of Longest Increasing Subsequences. Cambridge University Press, Cambridge (2014)CrossRefzbMATHGoogle Scholar
  5. 5.
    Albert, M.H., Golynski, A., Hamel, A.M., et al.: Longest increasing subsequences in sliding windows. Theoret. Comput. Sci. 321(2–3), 405–414 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Arlotto, A., Nguyen, V.V., Steele, J.M.: Optimal online selection of a monotone subsequence: a central limit theorem. Stochast. Process. Appl. 125(9), 3596–3622 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Nagarajan, V., Sviridenko, M.: Tight bounds for permutation flow shop scheduling. Math. Oper. Res. 34(2), 417–427 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Sitters, R.: Competitive analysis of preemptive single-machine scheduling. Oper. Res. Lett. 38(6), 585–588 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Nther, E., Maurer, O., Megow, N., et al.: A new approach to online scheduling: approximating the optimal competitive ratio. In: Twenty-Fourth ACM-SIAM Symposium on Discrete Algorithms, pp. 118–128. Society for Industrial and Applied Mathematics (2012)Google Scholar
  10. 10.
    Karhi, S., Shabtay, D.: On the optimality of the TLS algorithm for solving the online-list scheduling problem with two job types on a set of multipurpose machines. J. Comb. Optim. 26(1), 198–222 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of ManagementXi’an Jiaotong UniversityXi’anChina
  2. 2.The State Key Lab for Manufacturing Systems EngineeringXi’anChina
  3. 3.Department of Geography, Santa BarbaraUniversity of CaliforniaBerkeleyUSA

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