NP Completeness: Difference between revisions

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* [[Traveling Salesman Problem]]
* [[Traveling Salesman Problem]]
* <font color=darkkhaki>Local Search</font>
* <font color=darkkhaki>Local Search</font>
* [[The 2SAT Problem]]

Revision as of 04:01, 30 November 2021

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Overview

Almost all the algorithms mentioned so far have been polynomial-time algorithms, which is to say that on an input of size n, their worst running time is O(nk) for some constant k. Generally, we think of a problem that is solvable by a polynomial-time algorithm as tractable or easy. A problem that requires super-polynomial time is designated intractable or hard. There are also problems whose status is unknown: no polynomial-time algorithm has been yet discovered for them, nor has anyone yet been able to prove that no polynomial-time algorithm can exist for any of them. This class of problems is called NP-complete problems. The set of NP-complete problems has the property that if an efficient algorithm exists for any one of them, then efficient algorithms exist for all of them. There are methods to show that a problem is NP-complete, and if that is the case, an approximation algorithm instead of a polynomial-time algorithm, can be developed form it.

TODO.

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