Maintaining a Large Matching or a Small Vertex Cover

We consider the problem of maintaining a large matching or 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 data structure that simultaneously achieves a constant approximation factor and handles a sequence of k updates in k ? polylog(n) time. Previous data structures require a polynomial amount of computation per update. The starting point of our construction is a distributed algorithm of Parnas and Ron (Theor. Comput. Sci. 2007), which they designed for their sublinear-time approximation algorithm for the vertex cover size. This leads us to wonder whether there are other connections between sublinear algorithms and dynamic data structures.

• Type: Conference
• Year: 2010
• Where: STOC
• Authors: Krzysztof Onak and Ronitt Rubinfeld
• Keywords: Algorithms, Constant Approximation Factor, Small Vertex Cover, STOC 2010, Vertex Cover Size