Advertisement

A Stable Marriages Algorithm to Optimize Satisfaction and Equity

  • Nikom Suvonvorn
  • Bertrand Zavidovique
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4142)

Abstract

This paper deals with designing an algorithm for feature pairing in vision, based on the ”stable marriages” paradigm. Our SZ is an extension of the recently published BZ algorithm. BZ scans the so-called ”marriage table” to optimize global satisfaction and equity over all couples. It still gets about 5% unstable results in average. After a case study that sorts blocking situations into 4 types, we explain here how to resolve unstability in forcing blocking pairs to marry wrt. their type. SZ is compared to BZ and Gale-Shapley on 40000 instances of a 200 persons large population. An example of stereo reconstruction by SZ is given for illustration.

Keywords

Stable Match Stereo Match Global Satisfaction Feature Pairing Preference List 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Zavidovique, B., Suvonvorn, N., Seetharaman, G.S.: A novel representation and algorithms for (quasi) stable marriages. In: ICINCO 2005 (September 2005)Google Scholar
  2. 2.
    Suvonvorn, N., Bouchafa, S., Zavidovique, B.: Marrying level lines for stereo or motion. In: Kamel, M.S., Campilho, A.C. (eds.) ICIAR 2005. LNCS, vol. 3656, pp. 391–398. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Gale, D., Shapley, L.S.: College admissions and the stability of marriage. American Mathematical Monthly 69, 9–15 (1962)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Teo, C.-P., Sethuraman, J., Tan, W.-P.: Gale-shapley stable marriage problem revisited: Strategic issues and applications. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds.) IPCO 1999. LNCS, vol. 1610, pp. 429–438. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Hartke, S., Bianco, D., Larimer, A.: Stable matchings in the couples problem. Morehead Electronic Journal of Applicable Mathematics 2 (June 2001)Google Scholar
  6. 6.
    Manlove, D.F.: Stable marriage with ties and unacceptable partners. Technical Report TR-1999-29, Computing Science Department of Glasgow University (January 1999)Google Scholar
  7. 7.
    Kavitha, T., Mehlhorn, K., Michail, D., Paluch, K.: Strongly stable matchings in time o(nm) and extension to the hospitals-residents problem. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 222–233. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Abeledo, H., Rothblum, U.G.: Paths to marriage stability. Elsevier: Discrete Applied Mathematics 63(1-12) (1995)Google Scholar
  9. 9.
    McVitie, D.G., Wilson, L.B.: Three procedures for the stable marriage problem. Communications of the ACM 14(7), 491–492 (1971)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nikom Suvonvorn
    • 1
  • Bertrand Zavidovique
    • 1
  1. 1.Institut d’Electronique FondamentaleUniversité Paris 11Orsay

Personalised recommendations