Abstract
While the 3-dimensional analogue of Sperner’s problem in the plane was known to be complete in class PPAD, the complexity of 2D-SPERNER itself is not known to be PPAD-complete or not. In this paper, we settle this open problem proposed by Papadimitriou [9] fifteen years ago. The result also allows us to derive the computational complexity characterization of a discrete version of the 2-dimensional Brouwer fixed point problem, improving a recent result of Daskalakis, Goldberg and Papadimitriou [4]. Those hardness results for the simplest version of those problems provide very useful tools to the study of other important problems in the PPAD class.
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References
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Chen, X., Deng, X. (2006). On the Complexity of 2D Discrete Fixed Point Problem. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_43
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DOI: https://doi.org/10.1007/11786986_43
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