Before revision:  Our model is inspired from the Feige-Kilian model [FK01] which has been studied in many other works [  Ste17, MMT20]  . Our algorithm and analysis is on similar lines to the one studied for the Densest k-subgraph problem in the recent work of Khanna and Louis [KL20].
After revision:  Our model is inspired from the Feige-Kilian model [FK01] which has been studied in many other works [ Ste17, MMT20] for a variety of graph problems . Our algorithm and analysis is on similar lines to the one studied for the Densest k-subgraph problem in the recent work of Khanna and Louis [KL20].