# Polynomial-Time Reduction

I have read many resources, but I cannot understand what the polynomial-time reduction is. In everywhere, this is explained with standard-pattern sentences.

Please can anyone explain it in detailed version ?

• Possible duplicate of What does a polynomial time reduction mean? – Badr B Jun 2 '18 at 18:44
• There are many descriptions already. What didn't you understand about them? I'm not trying to be sarcastic -- it's just that, without some guidance about what you actually need, it seems quite likely that somebody will explain it to you and you'll say, "Sorry, I don't understand that, either." – David Richerby Jun 2 '18 at 20:02

In the vaguest sense you can think of a polynomial time reduction as a reduction that requires $O(n^k)$ steps (for a fixed k). So we require polynomial time in order to transform any instance of the "hard" problem into an instance of the new problem. Again the wiki page gives a description of different types of polynomial time reductions.