NP Completeness: Difference between revisions

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* https://www.coursera.org/learn/algorithms-npcomplete/lecture/ApF82/ananysis-of-dynamic-programming-heuristic
* https://www.coursera.org/learn/algorithms-npcomplete/lecture/ApF82/ananysis-of-dynamic-programming-heuristic
* https://www.coursera.org/learn/algorithms-npcomplete/lecture/YpJsR/the-maximum-cut-problem-i
* https://www.coursera.org/learn/algorithms-npcomplete/lecture/YpJsR/the-maximum-cut-problem-i
* https://www.coursera.org/learn/algorithms-npcomplete/lecture/ss1w9/the-maximum-cut-problem-ii
* https://www.coursera.org/learn/algorithms-npcomplete/lecture/mT2vp/principles-of-local-search-i


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Revision as of 23:48, 29 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.

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