Combinatorica
Testing Expansion in Bounded-Degree Graphs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Eigenvalues, Expanders And Superconcentrators
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Local graph exploration and fast property testing
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
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
SIAM Journal on Discrete Mathematics
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We study the problem of testing the expansion of graphs with bounded degree d in sublinear time. A graph is said to be an @a-expander if every vertex set U@?V of size at most 12|V| has a neighborhood of size at least @a|U|. We show that the algorithm proposed by Goldreich and Ron [9] (ECCC-2000) for testing the expansion of a graph distinguishes with high probability between @a-expanders of degree bound d and graphs which are -far from having expansion at least @W(@a^2). This improves a recent result of Czumaj and Sohler [3] (FOCS-07) who showed that this algorithm can distinguish between @a-expanders of degree bound d and graphs which are -far from having expansion at least @W(@a^2/logn). It also improves a recent result of Kale and Seshadhri [12] (ECCC-2007) who showed that this algorithm can distinguish between @a-expanders and graphs which are -far from having expansion at least @W(@a^2) with twice the maximum degree. Our methods combine the techniques of [3], [9] and [12].