$\alpha$-approximation

An $\alpha$-approximation algorithm for an approximation problem is a polynomial time algorithm that, for all instances of the problem produces a solution whose value is with in a factor of $\alpha$ of the value of an optimal solution. Further, we call $\alpha$ the performance guarantee of the algorithm. It is also called approximation ration or approximation factor of the algorithm. The $\alpha > 1$ is condition for minimization problems, and $\alpha < 1$ is criteria for maximization problems.