Consider the following problem :
Given a set of sets of integers, $\Sigma = \{S_i, i \in I\}$, and a set G, determine wether $\Sigma$ contains a partition of G, i.e. a set $J \subseteq I$ such that $G = \bigsqcup_{j\in J} S_j$.
This problem is (if i'm not mistaken) in NP.
I'm trying to determine wether this problem is in P (Or maybe NP-complete).
- Do you know if this problem is treated anywhere in the litterature (Algorithm or NP Completeness) ?
- Do you know any problems that are close to this one ?
I have tried to design a polynomial algorithm for the problem, but nothing working so far.