# Approximation algorithm

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Approximation algorithmаппроксимирующий алгоритм.

For the travelling salesman problem, as indeed for any other intractable problem it is useful to have a polynomial time algorithm which will produce, within known bounds, an approximation to the required result. Such algorithms are called approximation algorithms. Let $\,L$ be the value obtained (for example, this may be the length of a travelling salesman's circuit) by an approximation algorithm and let $\,L_{0}$ be an exact value. We require a performance guarantee for the approximation algorithm which could, for a minimisation problem, be stated in the form:

$1 \leq L/L_{0} \leq \alpha.$

For a maximisation problem we invert the ratio $\,L/L_{0}$. Of course, we would like $\,\alpha$ to be as close to one as possible.

Unfortunately, not every heuristic produces a useful approximation algorithm.