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NP-complete problems

These problems have something in common, you need to calculate every possible solution and pick the most optimal one.

They are expensive to calculate and it's usually better to use a simpler approximation algorithm (e.g., greedy algorithms).

Identify them

Can you restate your problem as the set-covering or the traveling-salesperson problems?

  • All combinations of "X".
  • Have to calculate every possible version of X because you can't break it down into smaller sub-problems.
  • Involves a sequence (e.g., cities like traveling salesperson) and it's hard to solve.
  • Involves a set (e.g., radio stations set-covering) and it's hard to solve.

Example problems

  • Traveling salesperson.
  • Set-covering.

Traveling salesperson vs shortest path

Calculating the shortest way to get from point A to point B can be done with Dijkstra's algorithm but if you want to find the shortest path that connects several points, that's the traveling-salesperson problem, which is NP-complete.