In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from L to H. That is, assuming a … 展开

A decision problem H is NP-hard when for every problem L in NP, there is a polynomial-time many-one reduction from L to H.
Another definition is to … 展开

NP-hard problems do not have to be elements of the complexity class NP. As NP plays a central role in computational complexity, it is used as the basis of several classes:
NP Class of computational decision problems for which any … 展开

• Lists of problems
• List of unsolved problems
• Reduction (complexity)
• Unknowability 展开

If P ≠ NP, then NP-hard problems could not be solved in polynomial time.
Some NP-hard optimization problems can be polynomial-time 展开

All NP-complete problems are also NP-hard (see List of NP-complete problems). For example, the optimization problem of finding the least-cost cyclic route through all nodes of a weighted graph—commonly known as the travelling salesman problem—is NP-hard. The 展开

NP-hard problems are often tackled with rules-based languages in areas including:
• Approximate computing
• Configuration
• Cryptography
• Data mining 展开