Every minor-closed property of sparse graphs is testable
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Testing the expansion of a graph
Information and Computation
Spanders: distributed spanning expanders
Proceedings of the 2010 ACM Symposium on Applied Computing
Expansion and the cover time of parallel random walks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Testing outerplanarity of bounded degree graphs
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Local graph exploration and fast property testing
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Tight bounds for the cover time of multiple random walks
Theoretical Computer Science
Quantum property testing for bounded-degree graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
An Expansion Tester for Bounded Degree Graphs
SIAM Journal on Computing
Rumor spreading and vertex expansion
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Rumor spreading and vertex expansion on regular graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
SIAM Journal on Discrete Mathematics
Principles of network computing
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Testing Closeness of Discrete Distributions
Journal of the ACM (JACM)
Spanders: Distributed spanning expanders
Science of Computer Programming
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We consider the problem of testing expansion in bounded degree graphs. We focus on the notion of vertex-expansion: an \alpha- \expander is a graph G = (V; E) in which every subset U \subseteq V of at most \left| V \right|/2 vertices has a neighborhood of size at least \alpha\cdot \left| U \right|. Our main result is that one can distinguish good expanders from graphs that are far from being weak expanders in time \mathop O\limits^\~ (\sqrt n ). We prove that the property testing algorithm proposed by Goldreich and Ron (2000) with appropriately set parameters accepts every \alpha- \exp ander with probability at least \frac{2} {3} and rejects every graph that is\in- far from an \alpha * - \exp ander with probability at least \frac{2} {3}, where \alpha * = \Theta (\frac{{\alpha ^2 }} {{d^2 \log (n/ \in )}}) and d is the maximum degree of the graphs. The algorithm assumes the bounded- degree graphs model with adjacency list graph representation and its running time is O(\frac{{d^2 \sqrt n \log (n/ \in )}} {{\alpha ^2\in ^3 }}).