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An Aside: Complexity Classes

Many of the above problems are solved, but some are not.

For the solved problems ...

  • some can be solved efficiently via a simple algorithm
  • some have polynomial worst-case performance (e.g. O(V2))
  • some have exponential worst-case performance (e.g. O(2V))
Classes of problems:
  • P = an algorithm can compute answer in polynomial time
  • NP = no P algorithm is known for solving the problem