https://doi.org/10.1140/epjb/e2014-40666-7
Regular Article
The physics of custody
1 Universidad Andres Bello,
Departamento de Ciencias Físicas, Av. República 252, 8370251
Santiago,
Chile
2 Departamento de Física, Facultad de
Ciencias, Universidad de Chile, Santiago, Chile
3 Universidad Andres Bello,
Departamento de Matemáticas, Av.
República 252, 8370251
Santiago,
Chile
a
e-mail: agomberoff@unab.cl
Received:
11
July
2013
Received in final form:
16
December
2013
Published online:
10
February
2014
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2014