Before revision:  In fact, the proposed algorithm implements a scheme EPTAS which, for any fixed \varepsilon\in(0,1), finds a (1-\varepsilon)-approximate solution of the considered problem in cubic time.
After revision:  In fact, the proposed algorithm implements an efficient PTAS which, for any fixed \varepsilon\in(0,1), finds a (1-\varepsilon)-approximate solution of the considered problem in cubic time.