# Converting an approximate algorithm for the minimization to the maximization form

I have a $$\rho$$-approximate algorithm for a minimization algorithm, where the objective is to minimize $$O$$ ($$\rho \geq 1$$ is some constant), such that the algorithm's solution is always within $$\rho$$ times the optimal. Is it possible to use this to get an approximate algorithm to maximize $$-O$$? What is the approximation ratio of this algorithm?

Thanks!

• Without any further restrictions, context or caveats, the answer is trivially yes. – orlp Oct 10 '18 at 9:41
• @orlp So what is the approximation ratio for this maximization problem? – Arani Oct 10 '18 at 9:43
• Am I missing something? Maximizing $-O$ is exactly the same as minimizing $O$ without any further changes, just negating the output. – orlp Oct 10 '18 at 9:44
• @orlp Yes, but having a $\rho$ approximation ratio does not make sense for a maximization problem, since for maximization the ratio should not be more than 1. But the ratio does not seem to be $1/\rho$ either. So I am confused about what the approximation ratio of the maximization version is. – Arani Oct 10 '18 at 9:47