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
A combinatorial characterization of the testable graph properties: it's all about regularity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Graph limits and parameter testing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Every minor-closed property of sparse graphs is testable
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Constant-Time Approximation Algorithms via Local Improvements
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Testing Hereditary Properties of Nonexpanding Bounded-Degree Graphs
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
New sublinear methods in the struggle against classical problems
New sublinear methods in the struggle against classical problems
An efficient partitioning oracle for bounded-treewidth graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
A near-optimal sublinear-time algorithm for approximating the minimum vertex cover size
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Constant-time algorithms for sparsity matroids
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Property testing in sparse directed graphs: strong connectivity and subgraph-freeness
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Testing subdivision-freeness: property testing meets structural graph theory
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
A quasi-polynomial time partition oracle for graphs with an excluded minor
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Testing linear-invariant function isomorphism
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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A property testing algorithm for a property Π in the bounded degree graph model[7] is an algorithm that, given access to the adjacency list representation of a graph G=(V,E) with maximum degree at most d, accepts G with probability at least 2/3 if G has property Π, and rejects G with probability at least 2/3, if it differs on more than ε dn edges from every d-degree bounded graph with property Π. A property is testable, if for every ε,d and n, there is a property testing algorithm Aε,n,d that makes at most q(ε,d) queries to an input graph of n vertices, that is, a non-uniform algorithm that makes a number of queries that is independent of the graph size. A k-disc around a vertex v of a graph G=(V,E) is the subgraph induced by all vertices of distance at most k from v. We show that the structure of a planar graph on large enough number of vertices, n, and with constant maximum degree d, is determined, up to the modification (insertion or deletion) of at most ε d n edges, by the frequency of k-discs for certain k=k(ε,d) that is independent of the size of the graph. We can replace planar graphs by any hyperfinite class of graphs, which includes, for example, every graph class that does not contain a set of forbidden minors. We use this result to obtain new results and improve upon existing results in the area of property testing. In particular, we prove that graph isomorphism is testable for every class of hyperfinite graphs, every graph property is testable for every class of hyperfinite graphs, every hyperfinite graph property is testable in the bounded degree graph model, A large class of graph parameters is approximable for hyperfinite graphs. Our results also give a partial explanation of the success of motifs in the analysis of complex networks.