Stable Marriage for Square Visual Puzzles May Yaari

Stable Marriage for Square Visual Puzzles May Yaari, Keren Ganon Advisor: Ohad Ben Shahar

n o i t c u d o r Int • What is a jigsaw puzzle? • Puzzle solving – NP-Complete problem • Can we use stable matches in order to find a solution?

s e h c t a M e l Stab ‘Marriage’:

m h t i r o g l A The Creating the graph • Two stable matches: Left and right part borders and top and bottom part borders

m h t i r o g l A The Creating the graph • Merge matches to graph: information about pair type (top-bottom or left-right) is kept separately

m h t i r o g l A The Extracting the tree • Create an MST from the graph:

m h t i r o g l A The Placing the parts

Frame • Problem - Puzzle boarders are paired - creates trailing match mistakes • Intermediate solution – add a frame to the original picture

e m a r F t u o With Placing the parts

e m a r F h t i W Placing the parts

a t a D d n Findings a 100, 00% 70, 00% 80, 00% 70, 00% 60, 00% With frame 50, 00% Without frame 40, 00% 30, 00% 20, 00% 10, 00% Average Match Accuracy 90, 00% 60, 00% 50, 00% 40, 00% Left-right Top-bottom 30, 00% 20, 00% 10, 00% 108 parts 192 parts 432 parts

k r o W r e Furth • Create separate segments instead of placing all parts on the same grid • Choose first node to place wisely • Weigh the graph edges differently • Find a way predict the puzzle’s frame