Before revision:  Due to the intractability to compute an exact MaxIS or its good approximation over dynamic graphs , this paper studies the problem to maintain a high-quality independent set, which is an approximation of the MaxIS , over dynamic graphs\ie .
After revision:  Due to the intractability to compute an exact MaxIS or its good approximation over dynamic graphs , this paper studies the problem of maintaining an approximate MaxIS over fully dynamic graphs, where 4 graph update operations are allowed\ie .