Skip to main content
SpringerLink
Log in
Book cover

Encyclopedia of Algorithms pp 885–888Cite as

Stable Partition Problem

2002; Cechlárová, Hajduková

  • Reference work entry

Keywords and Synonyms

In the economists community these models are often referred to as Coalition formation games [4,7], or Hedonic games [3,6,16]; some variants correspond to the Directed cycle cover problems [1]. Important special cases are the Stable Matching Problems [17].  . 

Problem Definition

In the Stable Partition Problem a set of participants has to be split into several disjoint sets called coalitions. The resulting partition should fulfill some stability requirements that take into account the preferences of participants.

Various variants of this problem arise if the participants are required to express their preferences over all the possible coalitions to which they could belong or when only preferences over other players are given and those are then extended to preferences over coalitions. Sometimes one seeks rather a permutation of players and the partition is given by the cycles of the permutation [1, 19].

Notation

An instance of the Stable Partition Problem (SPP for...

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   399.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Recommended Reading

  1. Abraham, D., Blum, A., Sandholm, T.: Clearing algorithms for barter exchange markets: Enabling nationwide kidney exchanges. EC'07, June 11–15, 2007, San Diego, California

    Google Scholar 

  2. Abraham, D., Cechlárová, K., Manlove, D., Mehlhorn, K.: Pareto-optimality in house allocation problems. In: Fleischer, R., Trippen, G. (eds.) Lecture Notes in Comp. Sci. Vol. 3341/2004, Algorithms and Computation, 14th Int. Symposium ISAAC 2004, pp. 3–15. Hong Kong, December 2004

    Google Scholar 

  3. Ballester, C.: NP-completeness in Hedonic Games. Games. Econ. Behav. 49(1), 1–30 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Banerjee, S., Konishi, H., Sönmez, T.: Core in a simple coalition formation game. Soc. Choice. Welf. 18, 135–153 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Biró, P., Cechlárová, K.: Inapproximability of the kidney exchange problem. Inf. Proc. Lett. 101(5), 199–202 (2007)

    Article  Google Scholar 

  6. Bogomolnaia, A., Jackson, M.O.: The Stability of Hedonic Coalition Structures. Games. Econ. Behav. 38(2), 201–230 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Burani, N., Zwicker, W.S.: Coalition formation games with separable preferences. Math. Soc. Sci. 45, 27–52 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cechlárová, K., Fleiner, T., Manlove, D.: The kidney exchange game. In: Zadnik-Stirn, L., Drobne, S. (eds.) Proc. SOR '05, pp. 77–83. Nova Gorica, September 2005

    Google Scholar 

  9. Cechlárová, K., Hajduková, J.: Stability testing in coalition formation games. In: Rupnik, V., Zadnik-Stirn, L., Drobne, S. (eds.) Proceedings of SOR'99, pp. 111–116. Predvor, Slovenia (1999)

    Google Scholar 

  10. Cechlárová, K., Hajduková, J.: Computational complexity of stable partitions with \( { \mathcal{B} } \)-preferences. Int. J. Game. Theory 31(3), 353–364 (2002)

    MATH  Google Scholar 

  11. Cechlárová, K., Hajduková, J.: Stable partitions with \( { \mathcal{W} } \)-preferences. Discret. Appl. Math. 138(3), 333–347 (2004)

    Article  MATH  Google Scholar 

  12. Cechlárová, K., Hajduková, J.: Stability of partitions under WB-preferences and BW-preferences. Int. J. Inform. Techn. Decis. Mak. Special Issue on Computational Finance and Economics. 3(4), 605–614 (2004)

    Google Scholar 

  13. Cechlárová, K., Romero-Medina, A.: Stability in coalition formation games. Int. J. Game. Theor. 29, 487–494 (2001)

    Article  MATH  Google Scholar 

  14. Cechlárová, K., Dahm, M., Lacko, V.: Efficiency and stability in a discrete model of country formation. J. Glob. Opt. 20(3–4), 239–256 (2001)

    Article  MATH  Google Scholar 

  15. Cechlárová, K., Lacko, V.: The Kidney Exchange problem: How hard is it to find a donor? IM Preprint A4/2006, Institute of Mathematics, P.J. Šafárik University, Košice, Slovakia, (2006)

    Google Scholar 

  16. Dimitrov, D., Borm, P., Hendrickx, R., Sung, S. Ch.: Simple priorities and core stability in hedonic games. Soc. Choice. Welf. 26(2), 421–433 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gusfield, D., Irving, R.W.: The Stable Marriage Problem. Structure and Algorithms. MIT Press, Cambridge (1989)

    MATH  Google Scholar 

  18. Roth, A., Sönmez, T., Ünver, U.: Kidney Exchange. Quarter. J. Econ. 119, 457–488 (2004)

    Article  MATH  Google Scholar 

  19. Shapley, L., Scarf, H.: On cores and indivisibility. J. Math. Econ. 1, 23–37 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  20. Yuan, Y.: Residence exchange wanted: A stable residence exchange problem. Eur. J. Oper. Res. 90, 536–546 (1996)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science, Institute of Mathematics, P.J. Šafárik University, Košice, Slovakia

    Katarína Cechlárová

Authors
  1. Katarína Cechlárová
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Cechlárová, K. (2008). Stable Partition Problem. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_397

Download citation

Publish with us

Policies and ethics

Search

Navigation