Before revision:  Our algorithms use a very simple scaling approach: we pick an absolute constant c} and optimize the function f(S)-c\cdot w(S) using a black-box application of standard algorithms , such as the classical Greedy algorithm and the single-threshold Greedy algorithm. These algorithms are based on recent works that use (time varying) scaling combined with classical algorithms such as the discrete and continuous Greedy algorithms (Feldman, WADS'19; Harshawet al. , ICML'19) .
After revision:  Our algorithms use a very simple scaling approach: we pick an absolute constant c} and optimize the function f(S)-c\cdot w(S) using a black-box application of standard algorithms et al. , ICML'19) .