Nothing Special   »   [go: up one dir, main page]

Skip to main content

Prophet Secretary for k-Knapsack and l-Matroid Intersection via Continuous Exchange Property

  • Conference paper
  • First Online:
Combinatorial Algorithms (IWOCA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12757))

Included in the following conference series:

  • 906 Accesses

Abstract

We study the k-knapsack and l-matroid constrained prophet secretary problem, which is a combinatorial prophet secretary problem whose feasible domain is the intersection of k-knapsack constraints and l-matroid constraints. Here, the prices of the items and the structure of the matroids are deterministic and known in advance, and the values of the items are stochastic and their distributions are known in advance. We derive a constant-factor approximation algorithm for this problem. We adapt Ehsani et al. (2018)’s technique for the matroid constraint to the knapsack constraint via continuous relaxation. For this purpose, we prove an “exchange property” of the knapsack constraint.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Albers, S., Khan, A., Ladewig, L.: Improved online algorithms for knapsack and gap in the random order model. In: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, pp. 22:1–22:23 (2019)

    Google Scholar 

  2. Azar, Y., Chiplunkar, A., Kaplan, H.: Prophet secretary: Surpassing the 1-1/e barrier. In: Proceedings of the 2018 ACM Conference on Economics and Computation, pp. 303–318. ACM (2018)

    Google Scholar 

  3. 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 

  4. Babaioff, M., Immorlica, N., Kleinberg, R.: Matroids, secretary problems, and online mechanisms. In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 434–443. Society for Industrial and Applied Mathematics (2007)

    Google Scholar 

  5. Brualdi, R.A.: Comments on bases in dependence structures. Bull. Aust. Math. Soc. 1(2), 161–167 (1969)

    Article  MathSciNet  Google Scholar 

  6. Correa, J., Foncea, P., Hoeksma, R., Oosterwijk, T., Vredeveld, T.: Posted price mechanisms for a random stream of customers. In: Proceedings of the 2017 ACM Conference on Economics and Computation, pp. 169–186 (2017)

    Google Scholar 

  7. Correa, J., Saona, R., Ziliotto, B.: Prophet secretary through blind strategies. In: Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1946–1961. SIAM (2019)

    Google Scholar 

  8. Dütting, P., Feldman, M., Kesselheim, T., Lucier, B.: Prophet inequalities made easy: stochastic optimization by pricing non-stochastic inputs. SIAM J. Comput. 49(3), 540–582 (2020)

    Article  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  10. Ehsani, S., Hajiaghayi, M., Kesselheim, T., Singla, S.: Prophet secretary for combinatorial auctions and matroids. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 700–714. SIAM (2018)

    Google Scholar 

  11. Esfandiari, H., Hajiaghayi, M.T., Liaghat, V., Monemizadeh, M.: Prophet secretary. SIAM J. Discrete Math. 31(3), 1685–1701 (2017)

    Article  MathSciNet  Google Scholar 

  12. Feldman, M., Svensson, O., Zenklusen, R.: A simple o (log log (rank))-competitive algorithm for the matroid secretary problem. In: Proceedings of the Twenty-sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1189–1201 (2014)

    Google Scholar 

  13. Feldman, M., Svensson, O., Zenklusen, R.: Online contention resolution schemes. In: Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1014–1033. SIAM (2016)

    Google Scholar 

  14. Kleinberg, R., Matthew, S., Weinberg, M.: prophet inequalities. In: Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing, pp. 123–136. ACM (2012)

    Google Scholar 

  15. Krengel, U., Sucheston, L.: Semiamarts and finite values. Bull. Am. Math. Soc. 83, 745–747 (1977)

    Article  MathSciNet  Google Scholar 

  16. Krengel, U., Sucheston, L.: On semiamarts, amarts, and processes with finite value. Probab. Banach Spaces 4, 197–266 (1978)

    MathSciNet  Google Scholar 

  17. Lachish, O.: O (log log rank) competitive ratio for the matroid secretary problem. In: 2014 IEEE 55th Annual Symposium on Foundations of Computer Science, pp. 326–335 (2014)

    Google Scholar 

  18. Samuel-Cahn, E.: Comparison of threshold stop rules and maximum for independent nonnegative random variables. Ann. Probab. 12, 1213–1216 (1984)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Soh Kumabe .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kumabe, S., Maehara, T. (2021). Prophet Secretary for k-Knapsack and l-Matroid Intersection via Continuous Exchange Property. In: Flocchini, P., Moura, L. (eds) Combinatorial Algorithms. IWOCA 2021. Lecture Notes in Computer Science(), vol 12757. Springer, Cham. https://doi.org/10.1007/978-3-030-79987-8_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-79987-8_30

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-79986-1

  • Online ISBN: 978-3-030-79987-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics