Given:

  • A set of available customers $c_1, c_2, \dots, c_n$.
  • A set of available foods $f_1, f_2, \dots, f_m$.
  • Each customer will choose a subset of the available food.

Problem:

  • Find the maximum number of customers that can be chosen, such that no two customers share the same food.

Question:

  • How to reduce the independent set problem to this problem, in order to prove that this is an NP-Complete problem ?
  • 2
    What have you tried? Where did you get stuck? – dkaeae Dec 6 at 14:02

Hint: try to reduce each vertex to a customer and each edge to an available food.

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