Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Discrete Applied Mathematics
On total functions, existence theorems and computational complexity
Theoretical Computer Science
Dividing and conquering the square
Discrete Applied Mathematics - Special issue: local optimization
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
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
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
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
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Bounds for Small-Error and Zero-Error Quantum Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Polynomial Degree vs. Quantum Query Complexity
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Quantum and classical query complexities of local search are polynomially related
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization
Theory of Computing Systems
ACM SIGACT News
Quantum and classical query complexities of local search are polynomially related
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
New upper and lower bounds for randomized and quantum local search
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Enhanced algorithms for local search
Information Processing Letters
Polynomial degree vs. quantum query complexity
Journal of Computer and System Sciences - Special issue on FOCS 2003
On the power of Ambainis lower bounds
Theoretical Computer Science
Quantum Separation of Local Search and Fixed Point Computation
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Adversary Lower Bounds for Nonadaptive Quantum Algorithms
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Quantum and Randomized Lower Bounds for Local Search on Vertex-Transitive Graphs
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
Quantum multiparty communication complexity and circuit lower bounds
Mathematical Structures in Computer Science
On the value of good advice: the complexity of A* search with accurate heuristics
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 2
Enhanced algorithms for Local Search
Information Processing Letters
Adversary lower bounds for nonadaptive quantum algorithms
Journal of Computer and System Sciences
A note on quantum algorithms and the minimal degree of ε-error polynomials for symmetric functions
Quantum Information & Computation
Lower bounds using kolmogorov complexity
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Lower bounds on matrix rigidity via a quantum argument
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
On the black-box complexity of sperner's lemma
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Linear vs. semidefinite extended formulations: exponential separation and strong lower bounds
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The time complexity of A* with approximate heuristics on multiple-solution search spaces
Journal of Artificial Intelligence Research
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The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube 0,1n, we show a lower bound of Ω(2n/4/n) on the number of queries needed by a quantum computer to solve this problem. More surprisingly, our approach, based on Ambainis's quantum adversary method, also yields a lower bound of Ω(2n/2/n2) on the problem's classical randomized query complexity. This improves and simplifies a 1983 result of Aldous. Finally, in both the randomized and quantum cases, we give the first nontrivial lower bounds for finding local minima on grids of constant dimension d≥3.