Skip to main content
SpringerLink
Log in
Book cover

International Computing and Combinatorics Conference

COCOON 2012: Computing and Combinatorics pp 98–108Cite as

Restricted Max-Min Fair Allocations with Inclusion-Free Intervals

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7434))

Abstract

We consider the restricted assignment version of the problem of fairly allocating a set of m indivisible items to n agents (also known as the Santa Claus problem). We study the variant where every item has some non-negative value and it can be assigned to an interval of players (i.e. to a set of consecutive players). Moreover, intervals are inclusion free. The goal is to distribute the items to the players and fair allocations in this context are those maximizing the minimum utility received by any agent. When every item can be assigned to any player a PTAS is known [Woe97]. We present a 1/2-approximation algorithm for the addressed more general variant with inclusion-free intervals.

Supported by the Swiss National Science Foundation Project N.200020-122110/1 ”Approximation Algorithms for Machine Scheduling Through Theory and Experiments III” and by Hasler Foundation Grant 11099.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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. Asadpour, A., Feige, U., Saberi, A.: Santa Claus Meets Hypergraph Matchings. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 10–20. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. Alon, N., Spencer, J.H.: The probabilistic method, 2nd edn. Wiley-Interscience, New York (2000)

    Book  MATH  Google Scholar 

  3. Asadpour, A., Saberi, A.: An approximation algorithm for max-min fair allocation of indivisible goods. In: STOC, pp. 114–121. ACM (2007)

    Google Scholar 

  4. Asadpour, A., Saberi, A.: An approximation algorithm for max-min fair allocation of indivisible goods. SIAM J. Comput. 39(7), 2970–2989 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bateni, M.H., Charikar, M., Guruswami, V.: Maxmin allocation via degree lower-bounded arborescences. In: STOC. ACM (2009)

    Google Scholar 

  6. Bezáková, I., Dani, V.: Allocating indivisible goods. SIGecom Exchanges 5(3), 11–18 (2005)

    Article  Google Scholar 

  7. Bansal, N., Sviridenko, M.: The santa claus problem. In: STOC, pp. 31–40. ACM (2006)

    Google Scholar 

  8. Chakrabarty, D., Chuzhoy, J., Khanna, S.: On allocating goods to maximize fairness. In: FOCS, pp. 107–116 (2009)

    Google Scholar 

  9. Feige, U.: On allocations that maximize fairness. In: SODA, pp. 287–293. ACM-SIAM (2008)

    Google Scholar 

  10. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman (1979)

    Google Scholar 

  11. Haeupler, B., Saha, B., Srinivasan, A.: New constructive aspects of the lovász local lemma. J. ACM 58(6), 28 (2011)

    Article  MathSciNet  Google Scholar 

  12. Halmos, P.R., Vaughan, H.E.: The marriage problem. American Journal of Mathematics, 214–215 (1950)

    Google Scholar 

  13. Khot, S., Ponnuswami, A.K.: Approximation Algorithms for the Max-Min Allocation Problem. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) RANDOM 2007 and APPROX 2007. LNCS, vol. 4627, pp. 204–217. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Lenstra, J.K., Shmoys, D.B., Tardos, É.: Approximation algorithms for scheduling unrelated parallel machines. In: FOCS, pp. 217–224. IEEE (1987)

    Google Scholar 

  15. Polacek, L., Svensson, O.: Quasi-polynomial local search for restricted max-min fair allocation. In: ICALP 2012 (2012)

    Google Scholar 

  16. Schrijver, A.: Theory of Linear and Integer Programming. John Wiley & Sons (1998)

    Google Scholar 

  17. Schrijver, A.: Combinatorial optimization: polyhedra and efficiency. Springer (2003)

    Google Scholar 

  18. Sgall, J.: Randomized on-line scheduling of parallel jobs. J. Algorithms 21(1), 149–175 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  19. Saha, B., Srinivasan, A.: A new approximation technique for resource-allocation problems. In: ICS, pp. 342–357. Tsinghua University Press (2010)

    Google Scholar 

  20. Shmoys, D.B., Tardos, É.: An approximation algorithm for the generalized assignment problem. Math. Program. 62, 461–474 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  21. Woeginger, G.: A polynomial-time approximation scheme for maximizing the minimum machine completion time. Operation Research Letters 20(4), 149–154 (1997)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IDSIA, Lugano, Switzerland

    Monaldo Mastrolilli & Georgios Stamoulis

Authors
  1. Monaldo Mastrolilli
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Georgios Stamoulis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of IT, University of Sydney, Building J12, 2006, Sydney, NSW, Australia

    Joachim Gudmundsson , Julián Mestre  & Taso Viglas ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mastrolilli, M., Stamoulis, G. (2012). Restricted Max-Min Fair Allocations with Inclusion-Free Intervals. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds) Computing and Combinatorics. COCOON 2012. Lecture Notes in Computer Science, vol 7434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32241-9_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-32241-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32240-2

  • Online ISBN: 978-3-642-32241-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation