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Compact Preference Representation in Stable Marriage Problems

  • Enrico Pilotto
  • Francesca Rossi
  • Kristen Brent Venable
  • Toby Walsh
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5783)

Abstract

The stable marriage problem has many practical applications in two-sided markets like those that assign doctors to hospitals, students to schools, or buyers to vendors. Most algorithms to find stable marriages assume that the participants explicitly expresses a preference ordering. This can be problematic when the number of options is large or has a combinatorial structure. We consider therefore using CP-nets, a compact preference formalism in stable marriage problems. We study the impact of this formalism on the computational complexity of stable marriage procedures, as well as on the properties of the solutions computed by these procedures. We show that it is possible to model preferences compactly without significantly increasing the complexity of stable marriage procedures and whilst maintaining the desirable properties of the matching returned.

Keywords

Partial Order Dependency Graph Stable Match Current Partner Stable Marriage 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Boutilier, C., Brafman, R.I., Domshlak, C., Hoos, H.H., Poole, D.: CP-nets: A tool for representing and reasoning with conditional ceteris paribus preference statements. J. Artif. Intell. Res. (JAIR) 21, 135–191 (2004)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Brafman, R.I., Chernyavsky, Y.: Planning with goal preferences and constraints. In: ICAPS, pp. 182–191 (2005)Google Scholar
  3. 3.
    Brafman, R.I., Domshlak, C., Kogan, T.: Compact value-function representations for qualitative preferences. In: UAI, pp. 51–59. AUAI Press (2004)Google Scholar
  4. 4.
    Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Amer. Math. Monthly 69 (1962)Google Scholar
  5. 5.
    Gusfield, D.: Three fast algorithms for four problems in stable marriage. SIAM Journal of Computing 16(1) (1987)Google Scholar
  6. 6.
    Gusfield, D., Irving, R.W.: The Stable Marriage Problem: Structure and Algorithms. MIT Press, Cambridge (1989)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Enrico Pilotto
    • 1
  • Francesca Rossi
    • 1
  • Kristen Brent Venable
    • 1
  • Toby Walsh
    • 2
  1. 1.Department of Pure and Applied MathematicsUniversity of PadovaItaly
  2. 2.NICTA and UNSWSydneyAustralia

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