What does the 2 in a 2-approximation algorithm mean?

Question

Does the 2 in a 2-approximation algorithm mean the solution is within 2*OPT or OPT/2?

Answer 1

Typically, we use $\alpha < 1$ for maximization problems, and $\alpha > 1$ for minimization problems, where $\alpha$ is the approximation guarantee. So, a $2$-approximation algorithm returns a solution whose cost is at most twice the optimal. But as always, to be absolutely sure, go back to the definitions of the text you are reading (if a definition is not available, assume this).