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hitting_set (826B)


      1 # Hitting set
      2 
      3 Given a family of sets on a universe, find a smallest subset of elements that
      4 intersects every set in the family
      5 
      6 The [dual] is the [set_cover] problem: find the smallest subset of sets whose
      7 union is equal to the universe. This duality is explained here
      8 <https://en.wikipedia.org/wiki/Set_cover_problem#Hitting_set_formulation>.
      9 Indeed, when considering the set of occurrences of every element for the set cover problem (the new sets), we want to find a subset of elements (the original sets) that intersects every new set (= the original elements), i.e., a subset of the original sets such that every original element is contained in a set of the subset.
     10 
     11 In [computational_geometry]: "stabbing" or "piercing" cf [nielsen2000fast]
     12 
     13 Up: [computational_problem] on [set]
     14 
     15 See also: [small_universe_hitting_set]