An NP complete problem is one where there is no know alo which can solve it in other than exponential time,ie the time taken to solve it increases to a power of the number of input parameters. At present, all known algorithms for NP-complete problems require time that is exponential in the problem size. It is unknown whether there are any faster algorithms. Therefore, to solve an NP-complete problem for any nontrivial problem size, one of the following approaches is used:

* Approximation: An algorithm that quickly finds a suboptimal solution that is within a certain (known) range of the optimal one.
* Probabilistic: An algorithm that provably yields good average runtime behavior for a given distribution of the problem instances—ideally, one that assigns low probability to "hard" inputs.
* Special cases: An algorithm that is provably fast if the problem instances belong to a certain special case. Fixed-parameter algorithms can be seen as an implementation of this approach.
* Heuristic: An algorithm that works "reasonably well" on many cases, but for which there is no proof that it is always fast (a rule of thumb, intuition).