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 to maintain a high-quality independent set, which is an approximation of the MaxIS , over dynamic graphs\ie, adding or deleting a vertex or an edge. Based on swap operation, we present a novel framework for maintaining an approximate maximum independent set which contains no k-swaps and make a deep analysis of performance ratio achieved by it .