The Complexity of Splitting Necklaces and Bisecting Ham Sandwiches

Aris Filos-Ratsikas; Paul W. Goldberg

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arXiv · 1805.12559

The Complexity of Splitting Necklaces and Bisecting Ham Sandwiches

Aris Filos-Ratsikas·Paul W. Goldberg

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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.

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BibTeX RIS

Aris Filos-Ratsikas, Paul W. Goldberg. 2018-05-31. The Complexity of Splitting Necklaces and Bisecting Ham Sandwiches. https://arxiv.org/abs/1805.12559

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