In the module about NP complete problems, we learned that if a polynomial algori

Question

In the module about NP complete problems, we learned that if a polynomial algorithm could be found for one NP complete problem, then that algorithm could be used to solve any problem in NP in polynomial time. My question is, can polynomial time approximation algorithms (like the ones we learned in this module) can be used in a similar way? That is, if we have one polynomial time approximation algorithm, can we use that algorithm as a subroutine to approximately solve other NP problems in polynomial time?

Explanation / Answer

Approximation algorithms are frequently connected with the NP-hard problems. Improbably it can ever be well-organized with the polynomial-time exact algorithms in solving NP-hard problems, where heuristics will find good and reasonable solutions in a quality of provable solution and with run-time bounds. Preferably, the approximation is ideal up to small constant factor and they are being gradually used for the problems, where they knew about the exact polynomial-time algorithms, but they are of too expensive due to the input size.

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