The physics of custody
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by
Andrés Gomberoff, Víctor Muñoz, Pierre Paul Romagnoli
2013
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.
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