A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
On the degree of polynomials that approximate symmetric Boolean functions (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Randomized algorithms
On the Power of Quantum Computation
SIAM Journal on Computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum lower bound for the collision problem
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Quantum Lower Bounds for the Collision and the Element Distinctness Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantum Algorithms for Element Distinctness
SIAM Journal on Computing
Quantum Query Complexity of Some Graph Problems
SIAM Journal on Computing
Negative weights make adversaries stronger
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Algorithms for Learning and Testing Juntas
Quantum Information Processing
Quantum Walk Algorithm for Element Distinctness
SIAM Journal on Computing
Quantum Algorithms for the Triangle Problem
SIAM Journal on Computing
Testing Expansion in Bounded-Degree Graphs
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
SIAM Journal on Computing
Testing the expansion of a graph
Information and Computation
Quantum walk based search algorithms
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Quantum property testing of group solvability
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
BQP and the polynomial hierarchy
Proceedings of the forty-second ACM symposium on Theory of computing
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
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
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We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time Õ(N1/3), beating the Ω(√N) classical lower bound. For testing expansion, we also prove an Ω(N1/4) quantum query lower bound, thus ruling out the possibility of an exponential quantum speedup. Our quantum algorithms follow from a combination of classical property testing techniques due to Goldreich and Ron, derandomization, and the quantum algorithm for element distinctness. The quantum lower bound is obtained by the polynomial method, using novel algebraic techniques and combinatorial analysis to accommodate the graph structure.