Single-Player and Two-Player Buttons & Scissors Games

被引：2

作者：

Burke, Kyle ^{[1
]}

Demaine, Erik D. ^{[2
]}

Gregg, Harrison ^{[3
]}

Hearn, Robert A. ^{[11
]}

Hesterberg, Adam ^{[2
]}

Hoffmann, Michael ^{[4
]}

Ito, Hiro

Kostitsyna, Irina ^{[6
]}

Leonard, Jody ^{[3
]}

Loeffler, Maarten ^{[7
]}

Santiago, Aaron ^{[3
]}

Schmidt, Christiane ^{[5
,8
]}

Uehara, Ryuhei ^{[9
]}

Uno, Yushi ^{[10
]}

Williams, Aaron ^{[3
]}

机构：

[1] Plymouth State Univ, Plymouth, NH 03264 USA

[2] MIT, Cambridge, MA 01230 USA

[3] Bard Coll Simons Rock, Great Barrington, MA 01230 USA

[4] Swiss Fed Inst Technol, Zurich, Switzerland

[5] Univ Elect Communicat, Chofu, Tokyo, Japan

[6] Univ Iibre Bruxelles, Brussels, Belgium

[7] Univ Utrecht, Utrecht, Netherlands

[8] Linkoping Univ, Norrkoping, Sweden

[9] Japan Adv Inst Sci & Technol, Nomi, Japan

[10] Osaka Prefecture Univ, Sakai, Osaka, Japan

[11] Portola Valley, Portola Valley, CA USA

来源：

DISCRETE AND COMPUTATIONAL GEOMETRY AND GRAPHS, JCDCGG 2015 | 2016年 / 9943卷

关键词：

D O I：

10.1007/978-3-319-48532-4_6

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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.

引用

页码：60 / 72

页数：13

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