Abstract
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 randomized 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.
Krzysztof Onak was supported in part by NSF grants 0732334 and 0728645. Ronitt Rubinfeld was supported in part by NSF grants 0732334 and 0728645, Marie Curie Reintegration grant PIRG03-GA-2008-231077, and the Israel Science Foundation grant nos. 1147/09 and 1675/09.
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Onak, K., Rubinfeld, R. (2010). Dynamic Approximate Vertex Cover and Maximum Matching. In: Goldreich, O. (eds) Property Testing. Lecture Notes in Computer Science, vol 6390. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16367-8_28
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DOI: https://doi.org/10.1007/978-3-642-16367-8_28
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