NP Completeness: Difference between revisions

From NovaOrdis Knowledge Base
Jump to navigation Jump to search
 
Line 27: Line 27:
* [[Traveling Salesman Problem]]
* [[Traveling Salesman Problem]]
* [[Local Search]]
* [[Local Search]]
** [[The Maximum Cut Problem]]
** [[The 2SAT Problem]]
** [[The 2SAT Problem]]

Latest revision as of 04:05, 30 November 2021

External

Internal

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.

Subjects