Single-Player and Two-Player Buttons & Scissors Games
Computational Complexity
2016-07-08 v1 Combinatorics
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 colors but polytime solvable for . Similarly the game is NP-complete if every color is used by at most buttons but polytime solvable for . 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.
Cite
@article{arxiv.1607.01826,
title = {Single-Player and Two-Player Buttons & Scissors Games},
author = {Kyle Burke and Erik D. Demaine and Harrison Gregg and Robert A. Hearn and Adam Hesterberg and Michael Hoffmann and Hiro Ito and Irina Kostitsyna and Jody Leonard and Maarten Löffler and Aaron Santiago and Christiane Schmidt and Ryuhei Uehara and Yushi Uno and Aaron Williams},
journal= {arXiv preprint arXiv:1607.01826},
year = {2016}
}
Comments
21 pages, 15 figures. Presented at JCDCG2 2015, Kyoto University, Kyoto, Japan, September 14 - 16, 2015