Single-Player and Two-Player Buttons & Scissors Games
Name
Single-player and two-player buttons scissors games.pdf
Size
3.79 MB
Format
Adobe PDF
Checksum (MD5)
7306ed93de21ee22465ab102836db6c0
Author(s)
Burke, Kyle
Gregg, Harrison
Hearn, Robert A.
Hoffmann, Michael
Ito, Hiro
Kostitsyna, Irina
Leonard, Jody
Löffler, Maarten
Santiago, Aaron
Schmidt, Christiane
Date Issued
November 2016
Journal
Discrete and Computational Geometry and Graphs
Publisher
Springer
Citation
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.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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/10.1007/978-3-319-48532-4_6
