NDLI: Noise Tolerance of Expanders and Sublinear Expansion Reconstruction

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Peres, Yuval Kale, Satyen Seshadhri, C.
Copyright Year	2013
Abstract	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 as possible. The graph $G'$ will be output by a distributed filter: this is a 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 also design sublinear time procedures to distinguish vertices of the expander part from those in the noise part and use this procedure in the reconstruction algorithm.
Starting Page	305
Ending Page	323
Page Count	19
File Format	PDF
ISSN	00975397
DOI	10.1137/110837863
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	1
Volume Number	42
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-02-14
Access Restriction	Subscribed
Subject Keyword	random walks Nonnumerical algorithms sublinear algorithms Analysis of algorithms and problem complexity Probability in computer science sublinear reconstruction Random walks on graphs graph expansion
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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