The physics of custody

  • Andrés Gomberoff
  • Víctor Muñoz
  • Pierre Paul Romagnoli
Regular Article

Abstract

Divorced individuals face complex situations when they have children with different ex-partners, or even more, when their new partners have children of their own. In such cases, and when kids spend every other weekend with each parent, a practical problem emerges: is it possible to have such a custody arrangement that every couple has either all of the kids together or no kids at all? We show that in general, it is not possible, but that the number of couples that do can be maximized. The problem turns out to be equivalent to finding the ground state of a spin glass system, which is known to be equivalent to what is called a weighted max-cut problem in graph theory, and hence it is NP-complete.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    S. Wasserman, K. Faust, Social Network Analysis: Methods and Applications, in Structural Analysis in the Social Sciences (Cambridge University Press, 1994), Vol. 8Google Scholar
  2. 2.
    S.P. Borgatti, A. Mehra, D.J. Brass, G. Labianca, Science 323, 892 (2009)ADSCrossRefGoogle Scholar
  3. 3.
    C. Castellano, S. Fortunato, V. Loreto, Rev. Mod. Phys. 81, 591 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    A. Szolnoki, N.-G. Xie, Y. Ye, M. Perc, Phys. Rev. E 87, 042805 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    P.S. Dodds, K.D. Harris, C.M. Danforth, Phys. Rev. Lett. 110, 158701 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    J. Török, G. Iñiguez, T. Yasseri, M. San Miguel, K. Kaski, J. Kertész, Phys. Rev. Lett. 110, 088701 (2013)ADSCrossRefGoogle Scholar
  7. 7.
    F. Heider, Psychol. Rev. 51, 358 (1944)CrossRefGoogle Scholar
  8. 8.
    D. Cartwright, F. Harary, Psychol. Rev. 63, 277 (1956)CrossRefGoogle Scholar
  9. 9.
    T. Antal, P.L. Krapivsky, S. Redner, Phys. Rev. E 72, 036121 (2005)ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    F. Radicchi, D. Vilone, H. Meyer-Ortmanns, Phys. Rev. E 75, 021118 (2007)ADSCrossRefMathSciNetGoogle Scholar
  11. 11.
    F. Radicchi, D. Vilone, S. Yoon, H. Meyer-Ortmanns, Phys. Rev. E 75, 026106 (2007)ADSCrossRefMathSciNetGoogle Scholar
  12. 12.
    S.A. Marvel, S.H. Strogatz, J.M. Kleinberg, Phys. Rev. Lett. 103, 198701 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    G. Facchetti, G. Iacono, C. Altafini, Phys. Rev. E 86, 036116 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    D. Sherrington, S. Kirkpatrick, Phys. Rev. Lett. 35, 1792 (1975)ADSCrossRefGoogle Scholar
  15. 15.
    D.R. Meyer, M. Cancian, S.T. Cook, Soc. Serv. Rev. 79, 577 (2005)CrossRefGoogle Scholar
  16. 16.
    A.S. Asratian, T.M. Denley, R. Häggkvist, Bipartite Graphs and Their Applications, in Cambridge Tracts in Mathematics (Cambridge University Press, 1998), Vol. 131Google Scholar
  17. 17.
    F. Barahona, M. Grötshel, M. Jünger, G. Reinelt, Oper. Res. 36, 493 (1988)CrossRefMATHGoogle Scholar
  18. 18.
    R.M. Karp, in Complexity of Computer Computations, edited by R.E. Miller, J.W. Thatcher (Plenum Press, New York, 1972), IBM Research Symposia Series, pp. 85–103Google Scholar
  19. 19.
    K.C. Ciesielski, J.K. Udupa, A.X. Falcao, P.A.V. Miranda, Journal of Mathematical Imaging and Vision 44, 375 (2012)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    U. Benlic, J.-K. Hao, Engineering Applications of Artifical Intelligence 26, 1162 (2013)CrossRefGoogle Scholar
  21. 21.
    Z.-B. Wang, S.-C. Fang, D.Y. Gao, W. Xing, Journal of Global Optimization 54, 341 (2012)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    G. Lin, W.-X. Zhu, J. Oper. Res. 196, 371 (2012)MATHMathSciNetGoogle Scholar
  23. 23.
    A.-F. Ling, C.-X. Xu, Numerical Algorithms 60, 435 (2012)CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    W.K. Shih, S. Wu, Y.S. Kuo, IEEE Trans. Comput. 39, 694 (1990)CrossRefMathSciNetGoogle Scholar
  25. 25.
    P. Berman, A.B. Kahng, D. Vidhani, A. Zelikovsky, in Workshop on Algorithms and Data Structures (WADS), edited by F.K. H.A. Dehne, A. Gupta, J.-R. Sack, R. Tamassia (Springer, Berlin, 1999), Vol. 1663 of Lecture Notes in Computer Science, pp. 25–36Google Scholar
  26. 26.
    F. Liers, G. Pardella, Computational Optimization and Applications 51, 323 (2012)CrossRefMATHMathSciNetGoogle Scholar
  27. 27.
    C. Dorius, Reconceptualizing Family Instability to Include Measures of Childbearing: The Practical Value of Assessing Multiple Partner Fertility, in Proceedings of the annual meeting for the Population Association of America, Washington, D.C., March 31-April 2, 2011 Google Scholar
  28. 28.
    K.B. Guzzo, F. Furstenberg Jr., Demography 44, 583 (2007)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Andrés Gomberoff
    • 1
  • Víctor Muñoz
    • 2
  • Pierre Paul Romagnoli
    • 3
  1. 1.Departamento de Ciencias FísicasUniversidad Andres BelloSantiagoChile
  2. 2.Departamento de Física, Facultad de CienciasUniversidad de ChileSantiagoChile
  3. 3.Departamento de MatemáticasUniversidad Andres BelloSantiagoChile

Personalised recommendations