Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Checking computations in polylogarithmic time
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
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
Approximations for the maximum acyclic subgraph problem
Information Processing Letters
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Tight bounds for the maximum acyclic subgraph problem
Journal of Algorithms
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
New sampling-based summary statistics for improving approximate query answers
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
On the Robustness of Functional Equations
SIAM Journal on Computing
Synopsis data structures for massive data sets
External memory algorithms
Testing problems with sublearning sample complexity
Journal of Computer and System Sciences
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Testing the Diameter of Graphs
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Improved Testing Algorithms for Monotonicity
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Regular Languages are Testable with a Constant Number of Queries
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Testing membership in parenthesis languages
Random Structures & Algorithms
Testing hypergraph colorability
Theoretical Computer Science - Automata, languages and programming
On testable properties in bounded degree graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the Query Complexity of Testing Orientations for Being Eulerian
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Property Testing: A Learning Theory Perspective
Foundations and Trends® in Machine Learning
Testing expansion in bounded-degree graphs
Combinatorics, Probability and Computing
Introduction to testing graph properties
Property testing
Property testing of massively parametrized problems – a survey
Property testing
Property testing of massively parametrized problems – a survey
Property testing
Contemplations on testing graph properties
Studies in complexity and cryptography
Testing Eulerianity and connectivity in directed sparse graphs
Theoretical Computer Science
On the query complexity of testing orientations for being Eulerian
ACM Transactions on Algorithms (TALG)
Property testing in sparse directed graphs: strong connectivity and subgraph-freeness
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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This article initiates the study of testing properties of directed graphs. In particular, the article considers the most basic property of directed graphs--acyclicity. Because the choice of representation affects the choice of algorithm, the two main representations of graphs are studied. For the adjacency-matrix representation, most appropriate for dense graphs, a testing algorithm is developed that requires query and time complexity of Õ(1/ε2), where ε is a distance parameter independent of the size of the graph. The algorithm, which can probe the adjacency matrix of the graph, accepts every graph that is acyclic, and rejects, with probability at least 2/3, every graph whose adjacency matrix should be modified in at least ε fraction of its entries so that it becomes acyclic. For the incidence list representation, most appropriate for sparse graphs, an Ω(|V|1/3) lower bound is proved on the number of queries and the time required for testing, where V is the set of vertices in the graph. Along with acyclicity, this article considers the property of strong connectivity. Contrasting upper and lower bounds are proved for the incidence list representation. In particular, if the testing algorithm can query on both incoming and outgoing edges at each vertex, then it is possible to test strong connectivity in Õ(1/ε) time and query complexity. On the other hand, if the testing algorithm only has access to outgoing edges, then Ω(√N) queries are required to test for strong connectivity.