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A 1-approximation is an approximation within a factor of 1. Basically that means that the solution is nearly exact. A 2-approximation would be no more than twice as bad as the optimal solution, and an n-aproximation would be no more than n times as bad as the optimal solution.

This is a common thing to use in randomized or approximate algorithms. For example, solving min-cut by assigning to 2 sets randomly is provably a 2-approximation.



I believe you mean Max-Cut can be 2 approximated with the trivial random algorithm. Min cut can be solved exactly, and that algorithm would give an expected n^2 approx factor (for min cut).




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