Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
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 Random Variables for Independence and Identity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Three theorems regarding testing graph properties
Random Structures & Algorithms
Functions that have read-twice constant width branching programs are not necessarily testable
Random Structures & Algorithms
Every monotone graph property is testable
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Testing versus estimation of graph properties
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The Difficulty of Testing for Isomorphism against a Graph That Is Given in Advance
SIAM Journal on Computing
A Characterization of the (natural) Graph Properties Testable with One-Sided Error
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Testing embeddability between metric spaces
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
Hierarchy Theorems for Property Testing
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Introduction to testing graph properties
Property testing
Hierarchy theorems for property testing
Property testing
Introduction to testing graph properties
Property testing
Hierarchy theorems for property testing
Property testing
Introduction to testing graph properties
Studies in complexity and cryptography
SIAM Journal on Discrete Mathematics
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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We deal with the question of how many queries are required to distinguish between the case that two graphs G and H on n vertices are isomorphic, and the case that they are ε-far, that is they differ in more than ε(n2) pairs for all possible bijections of their vertices. Querying is defined as probing the adjacency matrix of any one of the two graphs, i.e. asking if a pair of vertices forms an edge of the graph or not.We investigate both one-sided error and two-sided error testers under two possible settings: The first setting is where both graphs need to be queried; and the second setting is where one of the graphs is known to the algorithm in advance.We prove that the query complexity of the one-sided error testing problem is Θ(n3/2) if both graphs need to be queried, and that it is Θ(n) if one of the graphs is known in advance (where the Θ notation hides polylogarithmic factors in the upper bounds). For the two-sided error testers we prove that the query complexity is Θ(√n when one of the graphs is known in advance, and we show that the query complexity lies between Ω(n) and Õ(n5/4) if both G and H need to be queried. All of our algorithms are additionally non-adaptive, while all of our lower bounds apply for adaptive testers as well as non-adaptive ones.