Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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 properties of directed graphs: acyclicity and connectivity
Random Structures & Algorithms
Testing subgraphs in large graphs
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Testing subgraphs in directed graphs
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximating the Minimum Spanning Tree Weight in Sublinear Time
SIAM Journal on Computing
Every minor-closed property of sparse graphs is testable
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
Local Graph Partitions for Approximation and Testing
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Every property of hyperfinite graphs is testable
Proceedings of the forty-third annual ACM symposium on Theory of computing
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We study property testing in directed graphs in the bounded degree model, where we assume that an algorithm may only query the outgoing edges of a vertex, a model proposed by Bender and Ron [4]. As our first main result, we we present the first property testing algorithm for strong connectivity in this model, having a query complexity of $\ensuremath{\mathcal{O}}(n^{1-\epsilon/(3+\alpha)})$ for arbitrary α0; it is based on a reduction to estimating the vertex indegree distribution. For subgraph-freeness we give a property testing algorithm with a query complexity of $\ensuremath{\mathcal{O}}(n^{1-1/k})$, where k is the number of connected componentes in the queried subgraph which have no incoming edge. We furthermore take a look at the problem of testing whether a weakly connected graph contains vertices with a degree of least 3, which can be viewed as testing for freeness of all orientations of 3-stars; as our second main result, we show that this property can be tested with a query complexity of $\ensuremath{\mathcal{O}}(\sqrt{n})$ instead of, what would be expected, Ω(n2/3).