Maintaining a large matching and a small vertex cover

Authors:
Krzysztof Onak;Ronitt Rubinfeld
Affiliations:
Massachusetts Institute of Technology, Cambridge, MA, USA;MIT / Tel Aviv University, Cambridge, MA, USA
Venue:
Proceedings of the forty-second ACM symposium on Theory of computing
Year:
2010

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Abstract

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.