Filos-Ratsikas, A ORCID: 0000-0001-7868-8114 and Goldberg, PW
(2019)
The complexity of splitting necklaces and bisecting ham sandwiches.
In: STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, 2019-6-23 - 2019-6-26.
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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 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.
Item Type: | Conference or Workshop Item (Unspecified) |
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Additional Information: | 58 pages, 20 figures |
Uncontrolled Keywords: | PPA-Completeness, Necklace Splitting, Ham Sandwich, Consensus Halving |
Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
Depositing User: | Symplectic Admin |
Date Deposited: | 24 Jun 2021 10:19 |
Last Modified: | 18 Jan 2023 21:37 |
DOI: | 10.1145/3313276.3316334 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3127560 |