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An approximation algorithm is an algorithm that finds an approximate solution to a (typically NP-hard) problem. The quality of the algorithm is measured by how close to the actual optimum it performs. For example, it is a constant factor approximation algorithm if it always outputs a solution that is within a constant factor of the optimum. Hardness of approximation is one way to separate NP-hard problems.

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How to recover integer part from known fractional root part?

Using the structure in the continued fraction expansion of a square root provides a relatively straightforward approach: expand out the continued fraction of $f$ until you see an initial segment that …
Steven Stadnicki's user avatar