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2008 49th Annual IEEE Symposium on Foundations of Computer Science (2008)
Oct. 25, 2008 to Oct. 28, 2008
ISSN: 0272-5428
ISBN: 978-0-7695-3436-7
pp: 719-728
We consider the problem of online sublinear expander reconstruction and its relation to random walks in ``noisy" expanders. Given access to an adjacency list representation of a bounded-degree graph G, we want to convert this graph into a bounded-degree expander G' changing G as little aspossible. The graph G' will be output by a distributed filter: this is sublinear time procedure that given a query vertex, outputs all its neighbors in G', and can do so even in a distributed manner, ensuring consistency in all the answers.One of the main tools in our analysis is a result on the behavior of random walks in graph that are almost expanders: graphs that are formed by arbitrarily connecting a small unknown graph (the noise) to a large expander. We show that a random walk from almost any vertex in the expander part will have fast mixing properties, in the general setting of irreducible finite Markov chains. We alsodesign sublinear time procedures to distinguish vertices of the expander part from those in the noise part, and use this procedure in the reconstruction algorithm.
Expander reconstruction, Sublinear algorithms, Random Walks

Y. Peres, S. Kale and C. Seshadhri, "Noise Tolerance of Expanders and Sublinear Expander Reconstruction," 2008 49th Annual IEEE Symposium on Foundations of Computer Science(FOCS), vol. 00, no. , pp. 719-728, 2008.
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