scholarly journals Shotgun assembly of random jigsaw puzzles

2020 ◽  
Vol 56 (4) ◽  
pp. 998-1015
Author(s):  
Charles Bordenave ◽  
Uriel Feige ◽  
Elchanan Mossel
Keyword(s):  
Jigsaw Puzzles ◽  
Shotgun Assembly

scholarly journals A Linear Threshold for Uniqueness of Solutions to Random Jigsaw Puzzles

2019 ◽  
Vol 28 (2) ◽  
pp. 287-302
Author(s):  
ANDERS MARTINSSON
Keyword(s):  
High Probability ◽  
Jigsaw Puzzle ◽  
Uniqueness Of Solutions ◽  
Labeled Graphs ◽  
Linear Threshold ◽  
All Solutions ◽  
Rotationally Symmetric ◽  
Jigsaw Puzzles ◽  
Shotgun Assembly ◽  
Similar Solutions

We consider a problem introduced by Mossel and Ross (‘Shotgun assembly of labeled graphs’, arXiv:1504.07682). Suppose a random n × n jigsaw puzzle is constructed by independently and uniformly choosing the shape of each ‘jig’ from q possibilities. We are given the shuffled pieces. Then, depending on q, what is the probability that we can reassemble the puzzle uniquely? We say that two solutions of a puzzle are similar if they only differ by a global rotation of the puzzle, permutation of duplicate pieces, and rotation of rotationally symmetric pieces. In this paper, we show that, with high probability, such a puzzle has at least two non-similar solutions when 2 ⩽ q ⩽ 2e−1/2n, all solutions are similar when q ⩾ (2+ϵ)n, and the solution is unique when q = ω(n).

Shibboleths and Jigsaw Puzzles 

1995 ◽  
Vol 82 (3) ◽  
pp. 607-608 ◽  
Author(s):  
Burnell R. Brown
Keyword(s):  
Jigsaw Puzzles

Jigsaw Puzzles, Mosaics, and Civil War Battle Narratives

2007 ◽  
Vol 53 (3) ◽  
pp. 236-243
Author(s):  
Kenneth W. Noe
Keyword(s):  
Civil War ◽  
Jigsaw Puzzles
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