What does big O mean as a term of an approximation ratio?
The expression "$A(L) \le (1 + \varepsilon) \text{Opt}(L) + O(1/\varepsilon^2)$" is, as usual, shorthand for the following:


  There exist constants $c&gt;0$ and $\varepsilon_0&gt;0$ such that for all $\varepsilon$ with $0&lt;\varepsilon&lt;\varepsilon_0$, the inequality $A(L) \le (1 + \varepsilon) \text{Opt}(L) + c/\varepsilon^2$ holds.