| dc.contributor.author | Bordenave, Charles | |
| dc.contributor.author | Feige, Uriel | |
| dc.contributor.author | Mossel, Elchanan | |
| dc.date.accessioned | 2021-06-10T21:33:09Z | |
| dc.date.available | 2021-06-10T21:33:09Z | |
| dc.date.issued | 2020-01 | |
| dc.date.submitted | 2018-03 | |
| dc.identifier.issn | 1042-9832 | |
| dc.identifier.issn | 1098-2418 | |
| dc.identifier.uri | https://hdl.handle.net/1721.1/130928 | |
| dc.description.abstract | We consider the shotgun assembly problem for a random jigsaw puzzle, introduced by Mossel and Ross (2015). Their model consists of a puzzle—an n×n grid, where each vertex is viewed as a center of a piece. Each of the four edges adjacent to a vertex is assigned one of q colors (corresponding to “jigs,” or cut shapes) uniformly at random. Unique assembly refers to there being only one puzzle (the original one) that is consistent with the collection of individual pieces. We show that for any ε>0, if q ≥ n1+ε, then unique assembly holds with high probability. The proof uses an algorithm that assembles the puzzle in time nΘ(1/ε).22. | en_US |
| dc.description.sponsorship | NSF (Grant CCF-1320105 and DMS-1737944) | en_US |
| dc.description.sponsorship | ONR (Grant N00014-14-1-0823 and N00014-17-1-2598) | en_US |
| dc.description.sponsorship | Simons Foundation (Grant 328025 and Award 622132) | en_US |
| dc.language.iso | en | |
| dc.publisher | Wiley | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1002/rsa.20899 | en_US |
| dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
| dc.source | Prof. Mossel via Phoebe Ayers | en_US |
| dc.title | Shotgun assembly of random jigsaw puzzles | en_US |
| dc.type | Article | en_US |
| dc.identifier.citation | Bordenave, Charles et al. "Shotgun assembly of random jigsaw puzzles." Random Structures and Algorithms 56, 4 (January 2020): 998-1015. © 2020 Wiley Periodicals, Inc. | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
| dc.relation.journal | Random Structures and Algorithms | en_US |
| dc.eprint.version | Author's final manuscript | en_US |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
| eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
| dc.date.updated | 2021-06-09T16:54:21Z | |
| dspace.orderedauthors | Bordenave, C; Feige, U; Mossel, E | en_US |
| dspace.date.submission | 2021-06-09T16:54:22Z | |
| mit.journal.volume | 56 | en_US |
| mit.journal.issue | 4 | en_US |
| mit.license | OPEN_ACCESS_POLICY | |
| mit.metadata.status | Complete | |
