Single-Player and Two-Player Buttons & Scissors Games
Author(s)Burke, Kyle; Gregg, Harrison; Hearn, Robert A.; Hoffmann, Michael; Ito, Hiro; Kostitsyna, Irina; Leonard, Jody; Löffler, Maarten; Santiago, Aaron; Schmidt, Christiane; Uehara, Ryuhei; Uno, Yushi; Williams, Aaron; Demaine, Erik D; Hesterberg, Adam Classen; ... Show more Show less
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We study the computational complexity of the Buttons & Scissors game and obtain sharp thresholds with respect to several parameters. Specifically we show that the game is NP-complete for C=2 colors but polytime solvable for C=1. Similarly the game is NP-complete if every color is used by at most F=4 buttons but polytime solvable for F≤3. We also consider restrictions on the board size, cut directions, and cut sizes. Finally, we introduce several natural two-player versions of the game and show that they are PSPACE-complete.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Department of Mathematics
Discrete and Computational Geometry and Graphs
Burke, Kyle, et al. “Single-Player and Two-Player Buttons & Scissors Games.” Discrete and Computational Geometry and Graphs, edited by Jin Akiyama et al., vol. 9943, Springer International Publishing, 2016, pp. 60–72.
Author's final manuscript