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International Computing and Combinatorics Conference

COCOON 2021: Computing and Combinatorics pp 553–564Cite as

The Secretary Problem with Reservation Costs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13025))

Abstract

We introduce two variants of the secretary problem, where a reservation fee can be paid to keep candidates on a short-list instead of rejecting them on the spot. In the first model, the fee has to be paid only once and keeps the reservation forever. In the second model, the fee has to be paid in every round as long as the reservation is kept. We analyze the competitive ratio for both variants and present optimal, relatively simple strategies.

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References

  1. Albers, S., Ladewig, L.: New results for the \(k\)-secretary problem. In: 30th International Symposium on Algorithms and Computation, ISAAC. LIPIcs, vol. 149, pp. 18:1–18:19 (2019). https://doi.org/10.4230/LIPIcs.ISAAC.2019.18

  2. Babaioff, M., Immorlica, N., Kempe, D., Kleinberg, R.: A knapsack secretary problem with applications. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) APPROX/RANDOM -2007. LNCS, vol. 4627, pp. 16–28. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74208-1_2

    Chapter  Google Scholar 

  3. Babaioff, M., Immorlica, N., Kempe, D., Kleinberg, R.: Online auctions and generalized secretary problems. SIGecom Exch. 7(2), (2008). https://doi.org/10.1145/1399589.1399596

  4. Bianchi, M.P., Böckenhauer, H.-J., Brülisauer, T., Komm, D., Palano, B.: Online minimum spanning tree with advice. Int. J. Found. Comput. Sci. 29(4), 505–527 (2018). https://doi.org/10.1142/S0129054118410034

    Article  MathSciNet  MATH  Google Scholar 

  5. Bianchi, M.P., Böckenhauer, H.-J., Hromkovič, J., Krug, S., Steffen, B.: On the advice complexity of the online \(L(2,1)\)-coloring problem on paths and cycles. Theor. Comput. Sci. 554, 22–39 (2014). https://doi.org/10.1016/j.tcs.2014.06.027

    Article  MathSciNet  MATH  Google Scholar 

  6. Böckenhauer, H.-J., Burjons, E., Hromkovič, J., Lotze, H., Rossmanith, P.: Online simple knapsack with reservation costs. In: 38th International Symposium on Theoretical Aspects of Computer Science, STACS 2021. LIPIcs, vol. 187, pp. 16:1–16:18 (2021). https://doi.org/10.4230/LIPIcs.STACS.2021.16

  7. Böckenhauer, H.-J., Dobson, R., Krug, S., Steinhöfel, K.: On energy-efficient computations with advice. In: Xu, D., Du, D., Du, D. (eds.) COCOON 2015. LNCS, vol. 9198, pp. 747–758. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21398-9_58

    Chapter  Google Scholar 

  8. Böckenhauer, H.-J., Fuchs, J., Unger, W.: Exploring sparse graphs with advice (extended abstract). In: Epstein, L., Erlebach, T. (eds.) WAOA 2018. LNCS, vol. 11312, pp. 102–117. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-04693-4_7

    Chapter  Google Scholar 

  9. Böckenhauer, H.-J., Hromkovič, J., Komm, D., Královič, R., Rossmanith, P.: On the power of randomness versus advice in online computation. In: Bordihn, H., Kutrib, M., Truthe, B. (eds.) Languages Alive. LNCS, vol. 7300, pp. 30–43. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31644-9_2

    Chapter  Google Scholar 

  10. Böckenhauer, H.-J., Hromkovič, J., Komm, D., Krug, S., Smula, J., Sprock, A.: The string guessing problem as a method to prove lower bounds on the advice complexity. Theor. Comput. Sci. 554, 95–108 (2014). https://doi.org/10.1016/j.tcs.2014.06.006

    Article  MathSciNet  MATH  Google Scholar 

  11. Böckenhauer, H.-J., Hromkovič, J., Krug, S., Unger, W.: On the advice complexity of the online dominating set problem. Theor. Comput. Sci. 862, 81–96 (2021). https://doi.org/10.1016/j.tcs.2021.01.022

    Article  MathSciNet  MATH  Google Scholar 

  12. Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R.: On the advice complexity of the k-server problem. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6755, pp. 207–218. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22006-7_18

    Chapter  MATH  Google Scholar 

  13. Böckenhauer, H.-J., Komm, D., Královič, R., Královič, R., Mömke, T.: Online algorithms with advice: the tape model. Inf. Comput. 254, 59–83 (2017). https://doi.org/10.1016/j.ic.2017.03.001

    Article  MathSciNet  MATH  Google Scholar 

  14. Böckenhauer, H.-J., Komm, D., Královič, R., Rossmanith, P.: The online knapsack problem: advice and randomization. Theor. Comput. Sci. 527, 61–72 (2014). https://doi.org/10.1016/j.tcs.2014.01.027

    Article  MathSciNet  MATH  Google Scholar 

  15. Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)

    MATH  Google Scholar 

  16. Buchbinder, N., Jain, K., Singh, M.: Secretary problems via linear programming. Math. Oper. Res. 39(1), 190–206 (2014). https://doi.org/10.1287/moor.2013.0604

    Article  MathSciNet  MATH  Google Scholar 

  17. Cesa-Bianchi, N., Lugosi, G.: Prediction, Learning, and Games. Cambridge University Press, Cambridge (2006). https://doi.org/10.1017/CBO9780511546921

    Book  MATH  Google Scholar 

  18. Hubert Chan, T.-H., Chen, F., Jiang, S.H.-C.: Revealing optimal thresholds for generalized secretary problem via continuous LP: impacts on online \(k\)-item auction and bipartite \(k\)-matching with random arrival order. In: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2015, San Diego, CA, USA, 4–6 January 2015, pp. 1169–1188. SIAM (2015). https://doi.org/10.1137/1.9781611973730.78

  19. Daniely, A., Mansour, Y.: Competitive ratio vs regret minimization: Achieving the best of both worlds. In: Algorithmic Learning Theory, ALT 2019, 22–24 March 2019, Chicago, Illinois, USA. Proceedings of Machine Learning Research, vol. 98, pp. 333–368. PMLR (2019)

    Google Scholar 

  20. Dynkin, E.B.: The optimum choice of the instant for stopping a Markov process. Sov. Math. 4, 627–629 (1963)

    MATH  Google Scholar 

  21. Kleinberg, R.D.: A multiple-choice secretary algorithm with applications to online auctions. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2005, Vancouver, British Columbia, Canada, 23–25 January 2005, pp. 630–631. SIAM (2005)

    Google Scholar 

  22. Komm, D.: An Introduction to Online Computation - Determinism, Randomization, Advice. Texts in Theoretical Computer Science. An EATCS Series, Springer, Cham (2016). https://doi.org/10.1007/978-3-319-42749-2

    Book  Google Scholar 

  23. Lindley, D.V.: Dynamic programming and decision theory. J. R. Stat. Soc. Ser. C (Appl. Stat.) 10(1), 39–51 (1961). http://www.jstor.org/stable/2985407

  24. Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Commun. ACM 28(2), 202–208 (1985). https://doi.org/10.1145/2786.2793

    Article  MathSciNet  Google Scholar 

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Acknowledgement

We like to thank our anonymous referees for their useful comments that helped to improve the exposition of the paper.

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Authors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Elisabet Burjons, Matthias Gehnen, Henri Lotze, Daniel Mock & Peter Rossmanith

Authors
  1. Elisabet Burjons
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  2. Matthias Gehnen
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  3. Henri Lotze
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  4. Daniel Mock
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  5. Peter Rossmanith
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Corresponding author

Correspondence to Matthias Gehnen .

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Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Chi-Yeh Chen

  2. National Tsing Hua University, Hsinchu, Taiwan

    Wing-Kai Hon

  3. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  4. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

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Burjons, E., Gehnen, M., Lotze, H., Mock, D., Rossmanith, P. (2021). The Secretary Problem with Reservation Costs. In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_46

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  • DOI: https://doi.org/10.1007/978-3-030-89543-3_46

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  • Print ISBN: 978-3-030-89542-6

  • Online ISBN: 978-3-030-89543-3

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