4 research outputs found
Single-Player and Two-Player Buttons & Scissors Games
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.Comment: 21 pages, 15 figures. Presented at JCDCG2 2015, Kyoto University,
Kyoto, Japan, September 14 - 16, 201
Single-Player and Two-Player Buttons & Scissors Games
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