Maintaining a large matching and a small vertex cover

@inproceedings{Onak2010MaintainingAL,
  title={Maintaining a large matching and a small vertex cover},
  author={Krzysztof Onak and Ronitt Rubinfeld},
  booktitle={STOC},
  year={2010}
}
We consider the problem of maintaining a large matching and a small vertex cover in a dynamically changing graph. Each update to the graph is either an edge deletion or an edge insertion. We give the first randomized data structure that simultaneously achieves a constant approximation factor and handles a sequence of K updates in K*polylog(n) time, where n is the number of vertices in the graph. Previous data structures require a polynomial amount of computation per update. 

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