2013/05/04 by Andrés Gomberoff, Víctor Muñoz, Pierre Paul Romagnoli · 1 voice
Computer Science · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Limits and Structures in Graph Theory #Markov Chains and Monte Carlo Methods #cond-mat.stat-mech #cs.SI #physics.soc-ph
paper · pdf · doi:10.1140/epjb/e2014-40666-7
7 pages, 6 figures
arxiv published 2013/05/04 · arxiv created 2013/12/19 · openalex publication_date 2014/02/01 · arxiv updated 2015/06/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.