Single-Player and Two-Player Buttons & Scissors Games

(Extended Abstract)
  • Kyle Burke
  • Erik D. Demaine
  • Harrison Gregg
  • Robert A. Hearn
  • Adam Hesterberg
  • Michael Hoffmann
  • Hiro Ito
  • Irina Kostitsyna
  • Jody Leonard
  • Maarten Löffler
  • Aaron Santiago
  • Christiane Schmidt
  • Ryuhei Uehara
  • Yushi Uno
  • Aaron Williams
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9943)

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 \(F\le 3\). 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.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Kyle Burke
    • 1
  • Erik D. Demaine
    • 2
  • Harrison Gregg
    • 3
  • Robert A. Hearn
    • 11
  • Adam Hesterberg
    • 2
  • Michael Hoffmann
    • 4
  • Hiro Ito
    • 5
  • Irina Kostitsyna
    • 6
  • Jody Leonard
    • 3
  • Maarten Löffler
    • 7
  • Aaron Santiago
    • 3
  • Christiane Schmidt
    • 8
  • Ryuhei Uehara
    • 9
  • Yushi Uno
    • 10
  • Aaron Williams
    • 3
  1. 1.Plymouth State UniversityPlymouthUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA
  3. 3.Bard College at Simon’s RockGreat BarringtonUSA
  4. 4.ETH ZürichZürichSwitzerland
  5. 5.The University of Electro-CommunicationsChofuJapan
  6. 6.Université libre de BruxellesBrusselsBelgium
  7. 7.Universiteit UtrechtUtrechtNetherlands
  8. 8.Linköping UniversityNorrköpingSweden
  9. 9.Japan Advanced Institute of Science and TechnologyNomiJapan
  10. 10.Osaka Prefecture UniversitySakaiJapan
  11. 11.Portola ValleyUSA

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