Shotgun assembly of random jigsaw puzzles
Name
RandomJigSawr26Sep19.pdf
Description
Accepted version
Size
343.06 KB
Format
Adobe PDF
Checksum (MD5)
0c5ce5c1e22d878e1b643bbf87704dde
Author(s)
Bordenave, Charles
Feige, Uriel
Mossel, Elchanan
Date Issued
January 2020
Journal
Random Structures and Algorithms
Publisher
Wiley
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.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1002/rsa.20899
