The complexity of splitting necklaces and bisecting ham sandwiches
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 r...
| Main Authors: | , |
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| Format: | Conference item |
| Language: | English |
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Association for Computing Machinery
2019
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| _version_ | 1797056900755357696 |
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| author | Filos-Ratsikas, A Goldberg, PW |
| author_facet | Filos-Ratsikas, A Goldberg, PW |
| author_sort | Filos-Ratsikas, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T19:29:00Z |
| format | Conference item |
| id | oxford-uuid:1ccb8aa6-bed9-4d97-8e4a-696c206d83a7 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:29:00Z |
| publishDate | 2019 |
| publisher | Association for Computing Machinery |
| record_format | dspace |
| spelling | oxford-uuid:1ccb8aa6-bed9-4d97-8e4a-696c206d83a72022-03-26T11:07:29ZThe complexity of splitting necklaces and bisecting ham sandwichesConference itemhttp://purl.org/coar/resource_type/c_5794uuid:1ccb8aa6-bed9-4d97-8e4a-696c206d83a7EnglishSymplectic ElementsAssociation for Computing Machinery2019Filos-Ratsikas, AGoldberg, PWWe 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. |
| spellingShingle | Filos-Ratsikas, A Goldberg, PW The complexity of splitting necklaces and bisecting ham sandwiches |
| title | The complexity of splitting necklaces and bisecting ham sandwiches |
| title_full | The complexity of splitting necklaces and bisecting ham sandwiches |
| title_fullStr | The complexity of splitting necklaces and bisecting ham sandwiches |
| title_full_unstemmed | The complexity of splitting necklaces and bisecting ham sandwiches |
| title_short | The complexity of splitting necklaces and bisecting ham sandwiches |
| title_sort | complexity of splitting necklaces and bisecting ham sandwiches |
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