The complexity of splitting necklaces and bisecting ham sandwiches



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, 2019-06-23 - 2019-06-26.

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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)
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: 17 Nov 2021 08:10
DOI: 10.1145/3313276.3316334
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3127560