The physics of custody
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.
KeywordsStatistical and Nonlinear Physics
- 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
- 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
- 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
- 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
- 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