Skip to main content

Bucket Game with Applications to Set Multicover and Dynamic Page Migration

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3669))

Abstract

We present a simple two-person Bucket Game, based on throwing balls into buckets, and we discuss possible players’ strategies. We use these strategies to create an approximation algorithm for a generalization of the well known Set Cover problem, where we need to cover each element by at least k sets. Furthermore, we apply these strategies to construct a randomized algorithm for Dynamic Page Migration problem achieving the optimal competitive ratio against an oblivious adversary.

Extended abstract. The full version of this paper is available under http://wwwhni. upb.de/publikationen/.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bartal, Y., Charikar, M., Indyk, P.: On page migration and other relaxed task systems. In: Proc. of the 8th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 43–52 (1997)

    Google Scholar 

  2. Ben-David, S., Borodin, A., Karp, R.M., Tardos, G., Wigderson, A.: On the power of randomization in online algorithms. In: Proc. of the 22nd ACM Symp. on Theory of Computing (STOC), pp. 379–386 (1990)

    Google Scholar 

  3. Berman, P., DasGupta, B., Sontag, E.: Randomized approximation algorithms for set multicover problems with applications to reverse engineering of protein and gene networks. In: Jansen, K., Khanna, S., Rolim, J.D.P., Ron, D. (eds.) RANDOM 2004 and APPROX 2004. LNCS, vol. 3122, pp. 39–50. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Bienkowski, M., Dynia, M., Korzeniowski, M.: Improved algorithms for dynamic page migration. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 365–376. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Bienkowski, M., Korzeniowski, auf der Heide, F.M.: Fighting against two adversaries: Page migration in dynamic networks. In: Proc. of the 16th ACM Symp. on Parallelism in Algorithms and Architectures (SPAA), pp. 64–73 (2004)

    Google Scholar 

  6. Black, D.L., Sleator, D.D.: Competitive algorithms for replication and migration problems. Technical Report CMU-CS-89-201, Department of Computer Science, Carnegie-Mellon University (1989)

    Google Scholar 

  7. Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. In: Proc. of the 9th ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 228–248 (1998)

    Google Scholar 

  8. Johnson, D.S.: Approximation algorithms for combinatorial problems. In: Proc. of the 5th ACM Symp. on Theory of Computing (STOC), pp. 38–49 (1973)

    Google Scholar 

  9. Lovász, L.: On the ratio of the optimal integral and fractional covers. Discrete Mathematics 13, 383–390 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  10. Mahdian, M., Ye, Y., Zhang, J.: Improved approximation algorithms for metric facility location problems. In: Approximation Algorithms for Combinatorial Optimization Problems, pp. 229–242 (2002)

    Google Scholar 

  11. Rajagopalan, S., Vazirani, V.V.: Primal-dual RNC approximation algorithms for set cover and covering integer programs. SIAM Journal on Computing 28(2), 525–540 (1999)

    Article  MathSciNet  Google Scholar 

  12. Raz, R., Safra, S.: A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In: Proc. of the 29th ACM Symp. on Theory of Computing (STOC), pp. 475–484 (1997)

    Google Scholar 

  13. Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Communications of the ACM 28(2), 202–208 (1985)

    Article  MathSciNet  Google Scholar 

  14. Westbrook, J.: Randomized algorithms for multiprocessor page migration. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 7, 135–150 (1992)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bienkowski, M., Byrka, J. (2005). Bucket Game with Applications to Set Multicover and Dynamic Page Migration. In: Brodal, G.S., Leonardi, S. (eds) Algorithms – ESA 2005. ESA 2005. Lecture Notes in Computer Science, vol 3669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11561071_72

Download citation

  • DOI: https://doi.org/10.1007/11561071_72

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29118-3

  • Online ISBN: 978-3-540-31951-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics