average-case hardness

Average-case hardness refers to the difficulty of solving problems not just in the worst-case scenario, but for a typical or average instance of that problem. In computing and mathematics, a problem is considered average-case hard if, on average, there is no efficient method to solve it quickly. This contrasts with worst-case scenarios, where we only consider the most challenging instances. Understanding average-case hardness helps identify problems that may be practical for some inputs but still complex in more common situations, which can inform algorithm design and complexity theory.