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The P versus NP problem is a major unsolved problem in theoretical computer science.Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.
Euler diagram for P, NP, NP-complete, and NP-hard set of problems (excluding the empty language and its complement, which belong to P but are not NP-complete) Main article: P versus NP problem The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time ), an algorithm ...
A problem p in NP is NP-complete if every other problem in NP can be transformed (or reduced) into p in polynomial time. [citation needed] It is not known whether every problem in NP can be quickly solved—this is called the P versus NP problem.
Thus the class of NP-complete problems contains the most difficult problems in NP, in the sense that they are the ones most likely not to be in P. Because the problem P = NP is not solved, being able to reduce a known NP-complete problem, Π 2 {\displaystyle \Pi _{2}} , to another problem, Π 1 {\displaystyle \Pi _{1}} , would indicate that ...
Euler diagram for P, NP, NP-complete, and NP-hard set of problems. Under the assumption that P ≠ NP, the existence of problems within NP but outside both P and NP-complete was established by Ladner. [1] In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems.
If P and NP are different, then there exist decision problems in the region of NP that fall between P and the NP-complete problems. (If P and NP are the same class, then NP-intermediate problems do not exist because in this case every NP-complete problem would fall in P, and by definition, every problem in NP can be reduced to an NP-complete ...
Lorden suggested using P vs. NP. [4] P vs. NP describes the length of time needed to solve a problem as compared with the number of steps in the problem. Generally, the length of time increases as the numbers of steps increase.
Quadratic programming (NP-hard in some cases, P if convex) Subset sum problem [3]: SP13 Variations on the Traveling salesman problem. The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric.