The Complexity of Splitting Necklaces and Bisecting Ham Sandwiches
Abstract
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 M\"obius 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.
Keywords
Cite
@article{arxiv.1805.12559,
title = {The Complexity of Splitting Necklaces and Bisecting Ham Sandwiches},
author = {Aris Filos-Ratsikas and Paul W. Goldberg},
journal= {arXiv preprint arXiv:1805.12559},
year = {2018}
}
Comments
58 pages, 20 figures