Algorithms for random generation and counting: a Markov chain approach
Algorithms for random generation and counting: a Markov chain approach
Randomized algorithms
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing Expansion in Bounded-Degree Graphs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
A Characterization of the (Natural) Graph Properties Testable with One-Sided Error
SIAM Journal on Computing
An Expansion Tester for Bounded Degree Graphs
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Testing Hereditary Properties of Nonexpanding Bounded-Degree Graphs
SIAM Journal on Computing
A Combinatorial Characterization of the Testable Graph Properties: It's All About Regularity
SIAM Journal on Computing
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Principles of network computing
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
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We consider the problem of testing graph expansion (either vertex or edge) in the bounded degree model [O. Goldreich and D. Ron, On Testing Expansion in Bounded-Degree Graphs, Technical report TR00-020, ECCC, Potsdam, Germany, 2000]. We give a property tester that takes as input a graph with degree bound $d$, an expansion bound $\alpha$, and a parameter $\varepsilon0$. The tester accepts the graph with high probability if its expansion is more than $\alpha$, and rejects it with high probability if it is $\varepsilon$-far from any graph with expansion $\alpha'$ with degree bound $d$, where $\alpha'0$.