# NP-Hardness Problems **NP-hardness** (non-deterministic polynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP". More precisely, a problem H is NP-hard when every problem L in NP can be reduced in polynomial time to H; that is, assuming a solution for H takes 1 unit time, we can use H‎'s solution to solve L in polynomial time. As a consequence, finding a polynomial algorithm to solve any NP-hard problem would give polynomial algorithms for all the problems in NP, which is unlikely as many of them are considered difficult. A common misconception is that the NP in "NP-hard" stands for "non-polynomial" when in fact it stands for "**N**on-deterministic **P**olynomial acceptable problems". Although it is suspected that there are no polynomial-time algorithms for NP-hard problems, this has not been proven. Moreover, the class P in which all problems can be solved in polynomial time, is contained in the NP class. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://alfredo-reyes-montero.gitbook.io/metaheuristics/optimization/readme/introduction/np-hard-problems.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.