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Diffusion Limits in the Online Subsequence Selection Problems

Authors Alexander Gnedin, Amirlan Seksenbayev

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Alexander Gnedin
  • Queen Mary, University of London, UK
Amirlan Seksenbayev
  • Queen Mary, University of London, UK

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Alexander Gnedin and Amirlan Seksenbayev. Diffusion Limits in the Online Subsequence Selection Problems. In 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 159, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.AofA.2020.14

Abstract

In the stochastic sequential optimisation problems it is of interest to study features of strategies more delicate than just their performance measure. In this talk we focus on variations of the online monotone subsequence and bin packing problems, where it is possible to give a fairly explicit asymptotic description of the selection processes under strategies that are sufficiently close to optimality. We show that the transversal fluctuations of the shape and the length of selected subsequence approach Gaussian functional limits that are very different from their counterparts in the offline problem, where the full set of data can be used in selection algorithms.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Markov processes
Keywords
  • sequential optimisation
  • longest increasing subsequence
  • bin packing
  • fluctuations in the selection process
  • functional limit

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References

  1. A. Arlotto, V.V. Nguyen, and J.M. Steele. Optimal online selection of a monotone subsequence: a central limit theorem. Stochastic Process. Appl., 125:3596-3622, 2015. Google Scholar
  2. A. Arlotto, Y. Wei, and X. Xie. A O(log n)-optimal policy for the online selection of a monotone subsequence from a random sample. Random Structures Algorithms, 52:41-53, 2018. Google Scholar
  3. S. Asmussen. Applied Probability and Queues. Springer, 2003. Google Scholar
  4. Y.M. Baryshnikov and A.V. Gnedin. Sequential selection of an increasing sequence from a multidimensional random sample. Ann. Probab., 10(1):258-267, 2000. Google Scholar
  5. A. Borovkov. Probability Theory. Springer, 2013. Google Scholar
  6. F.T. Bruss and F. Delbaen. Optimal rules for the sequential selection of monotone subsequences of maximum expected length. Stoch. Proc. Appl., 96:313-342, 2001. Google Scholar
  7. F.T. Bruss and F. Delbaen. A Central Limit Theorem for the optimal selection process for monotone subsequences of maximum expected length. Stoch. Proc. Appl., 114:287-311, 2004. Google Scholar
  8. M. Nica D. Dauvergne and B. Virág. Uniform convergence to the airy line ensemble. ArXiv e-print, 2019. URL: http://arxiv.org/abs/1907.10160.
  9. L. Flatto E.G. Coffman and R.R. Weber. Optimal selection of stochastic intervals under a sum constraint. Adv. Appl. Prob., 19:454-473, 2015. Google Scholar
  10. A. Gnedin. Sequential selection of an increasing subsequence from a sample of random size. J. Appl. Probab., 36(4):1074-–1085, 1999. Google Scholar
  11. A. Gnedin and A. Seksenbayev. Asymptotics and renewal approximation in the online selection of increasing subsequence. ArXiv e-print, 2019. URL: http://arxiv.org/abs/1904.11213.
  12. K. Johansson. The longest increasing subsequence in a random permutation and a unitary random matrix model. Math. Res. Lett., 5(1-2):63-82, 1998. Google Scholar
  13. O. Kallenberg. Foundations of modern probability. Springer, 2002. Google Scholar
  14. M. B. Marcus and J. Rosen. Markov processes, Gaussian processes and local time. CUP, 2006. Google Scholar
  15. M. Joseph P. S. Dey and R. Peled. Longest increasing path within the critical strip. ArXiv e-print, 2018. URL: http://arxiv.org/abs/1808.08407.
  16. W. Rhee and M. Talagrand. A note on the selection of random variables under a sum constraint. J. Appl. Probab., 28(4):919-923, 1991. Google Scholar
  17. D. Romik. The Surprising Mathematics of Longest Increasing Subsequences. Cambridge University Press, 2015. Google Scholar
  18. S.M. Samuels and J.M. Steele. Optimal sequential selection of a monotone sequence from a random sample. Ann. Probab., 9(6):937-947, 1981. Google Scholar
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