2018/05/31 by Filos-Ratsikas, Aris, Goldberg, Paul W.
#Artificial Intelligence (cs.AI) #Computational Complexity (cs.CC) #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1805.12559
We resolve the computational complexity of two problems known as NECKLACE-SPLITTING and DISCRETE HAM SANDWICH, showing that they are PPA-complete. For NECKLACE SPLITTING, this result is specific to the important special case in which two thieves share the necklace. We do this via a PPA-completeness result for an approximate version of the CONSENSUS-HALVING problem, strengthening our recent result that the problem is PPA-complete for inverse-exponential precision. At the heart of our construction is a smooth embedding of the high-dimensional Möbius strip in the CONSENSUS-HALVING problem. These results settle the status of PPA as a class that captures the complexity of "natural" problems whose definitions do not incorporate a circuit.