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    Wikipedia
    https://en.wikipedia.org › wiki › NP-hardness

    NP-hardness - Wikipedia

    • A simple example of an NP-hard problem is the subset sum problem. Informally, if H is NP-hard, then it is at least as difficult to solve as the problems in NP. However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP, but they are probably not NP-hard (unless ...… 展开

    Overview

    In computational complexity theory, a computational problem H is called NP-hard if, for every problem L which c… 展开

    Definition

    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 require that there be a polynomial-tim… 展开

    Consequences

    If P ≠ NP, then NP-hard problems could not be solved in polynomial time.
    Some NP-hard optimization problems can be polynomial-time approximated up to some constant approximation ratio (in particular, those in … 展开

    Examples

    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 … 展开

    NP-naming convention

    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 com… 展开

    Application areas

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

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