On total functions, existence theorems and computational complexity
Theoretical Computer Science
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 complexity of 2d discrete fixed point problem
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Discrete Fixed Points: Models, Complexities, and Applications
Mathematics of Operations Research
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Tucker's lemma states that if we triangulate the unit disc centered at the origin and color the vertices with {1, 驴 1,2, 驴 2} in an antipodal way (if |z| = 1, then the sum of the colors of z and 驴 z is zero), then there must be an edge for which the sum of the colors of its endpoints is zero. But how hard is it to find such an edge? We show that if the triangulation is exponentially large and the coloring is determined by a deterministic Turing-machine, then this problem is PPAD-complete which implies that there is not too much hope for a polynomial algorithm.