Approximation ratio ($\alpha$)

For maximization, an approximation ratio $\alpha \in (0,1]$ means the returned feasible value is at least $\alpha$ times the optimal value on every permitted instance. Some conventions instead report its reciprocal; specify the convention.

For a minimization problem with positive optimum, this convention measures the relative excess $(\mathrm{ALG}-\mathrm{OPT})/\mathrm{OPT}$. An epsilon-approximation always returns a feasible solution with excess at most $\epsilon$. A multiplicative-ratio convention instead reports $1+\epsilon$. State the convention explicitly rather than treating these two numbers as interchangeable.