A separator theorem for graphs of bounded genus
Journal of Algorithms
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
On the complexity of the parity argument and other inefficient proofs of existence
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
On the Power of Quantum Computation
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
The relative complexity of NP search problems
Journal of Computer and System Sciences
Sperner's lemma and robust machines
Computational Complexity
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
Polynomial Degree vs. Quantum Query Complexity
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Lower bounds for local search by quantum arguments
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
Relativized NP Search Problems and Propositional Proof Systems
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Lower Bounds for Randomized and Quantum Query Complexity Using Kolmogorov Arguments
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
On graph-theoretic lemmata and complexity classes
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
All quantum adversary methods are equivalent
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Quantum Separation of Local Search and Fixed Point Computation
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
On the complexity of 2D discrete fixed point problem
Theoretical Computer Science
Discrete Fixed Points: Models, Complexities, and Applications
Mathematics of Operations Research
On the complexity of the sperner lemma
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Lattice embedding of direction-preserving correspondence over integrally convex set
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
A simplicial approach for discrete fixed point theorems
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Algorithmic Solutions for Envy-Free Cake Cutting
Operations Research
Algorithmic Solutions for Envy-Free Cake Cutting
Operations Research
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We present several results on the complexity of various forms of Sperner's Lemma in the black-box model of computing. We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension. The query complexity of our algorithm is linear in the separation number of the skeleton graph of the manifold and the size of its boundary. As a corollary we get an $O(\sqrt{n})$ deterministic query algorithm for the black-box version of the problem 2D-SPERNER, a well studied member of Papadimitriou's complexity class PPAD. This upper bound matches the $\Omega(\sqrt{n})$ deterministic lower bound of Crescenzi and Silvestri. The tightness of this bound was not known before. In another result we prove for the same problem an $\Omega(^{4}\sqrt{n})$ lower bound for its probabilistic, and an $\Omega(^{8}\sqrt{n})$ lower bound for its quantum query complexity, showing that all these measures are polynomially related.