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Dynamic Approximate Vertex Cover and Maximum Matching

Author(s)
Onak, Krzysztof; Rubinfeld, Ronitt
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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.
Date issued
2010-10
URI
http://hdl.handle.net/1721.1/73896
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
Property Testing
Publisher
Springer Berlin / Heidelberg
Citation
Onak, Krzysztof, and Ronitt Rubinfeld. “Dynamic Approximate Vertex Cover and Maximum Matching.” Property Testing. Ed. Oded Goldreich. LNCS Vol. 6390. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. 341–345.
Version: Author's final manuscript
ISBN
978-3-642-16366-1
ISSN
0302-9743
1611-3349

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