Polynomial-time reduction

In computational complexity theory, a polynomial-time reduction is a method of solving one problem by means of a hypothetical subroutine for solving a different problem (that is, a reduction), that uses polynomial time excluding the time within the subroutine. There are several different types of polynomial-time reduction, depending on the details of how the subroutine is used. Intuitively, a polynomial-time reduction proves that the first problem is no more difficult than the second one, because whenever an efficient algorithm exists for the second problem, one exists for the first problem as well. Polynomial-time reductions are frequently used in complexity theory for defining both complexity classes and complete problems for those classes.