Exponential lower bounds for finding Brouwer fixed points
Journal of Complexity
Sperner's lemma and robust machines
Computational Complexity
On algorithms for discrete and approximate brouwer fixed points
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
On the complexity of 2d discrete fixed point problem
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
Sperner's lemma and zero point theorems on a discrete simplex and a discrete simplotope
Discrete Applied Mathematics
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We present a new discrete fixed point theorem based on a novel definition of direction-preserving maps over simplicial structures. We show that the result is more general and simpler than the two recent discrete fixed point theorems by deriving both of them from ours. The simplicial approach applied in the development of the new theorem reveals a clear structural comparison with the classical approach for the continuous case.