..  _Problem_Set_Covering:

Minimum Set Cover Problem
=========================

Minimum Set Cover Problem is the NP-hard problem often found in combinatorial optimization. The main goal is to find minimal number of subsets that cover initial set.

It is enlisted in  `NP Compendium <https://www.csc.kth.se/tcs/compendium/node146.html>`_ .

Problem Definition
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- **Instance:** An initial set U (called universe), and a set S = {S1, S2, ..., Sn} ⊆ U of subsets of U.

- **Solution:**  Find a set of subsets from S that cover entire set U.

- **Measure:** Minimize the number of sets found in a solution.

* Minimum Multi Cut Problem. Problem is represented with class :ref:`MinSetCoverProblemProblem<py_set_covering_problem>`.