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...
| Main Authors: | , |
|---|---|
| Format: | Conference item |
| Published: |
Association for Computing Machinery
2019
|
| _version_ | 1797093510686441472 |
|---|---|
| author | Filos-Ratsikas, A Goldberg, P |
| author_facet | Filos-Ratsikas, A Goldberg, P |
| 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 Mobius 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 | 2024-03-07T04:01:31Z |
| format | Conference item |
| id | oxford-uuid:c4bc003f-e4b0-4571-acd7-0a6456fc796c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:01:31Z |
| publishDate | 2019 |
| publisher | Association for Computing Machinery |
| record_format | dspace |
| spelling | oxford-uuid:c4bc003f-e4b0-4571-acd7-0a6456fc796c2022-03-27T06:25:43ZThe complexity of splitting necklaces and bisecting ham sandwichesConference itemhttp://purl.org/coar/resource_type/c_5794uuid:c4bc003f-e4b0-4571-acd7-0a6456fc796cSymplectic Elements at OxfordAssociation for Computing Machinery2019Filos-Ratsikas, AGoldberg, PWe 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 Mobius 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, P 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 |
| work_keys_str_mv | AT filosratsikasa thecomplexityofsplittingnecklacesandbisectinghamsandwiches AT goldbergp thecomplexityofsplittingnecklacesandbisectinghamsandwiches AT filosratsikasa complexityofsplittingnecklacesandbisectinghamsandwiches AT goldbergp complexityofsplittingnecklacesandbisectinghamsandwiches |