License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2018.11
URN: urn:nbn:de:0030-drops-88029
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Bosboom, Jeffrey ; Demaine, Erik D. ; Rudoy, Mikhail

Computational Complexity of Generalized Push Fight

LIPIcs-FUN-2018-11.pdf (1 MB)


We analyze the computational complexity of optimally playing the two-player board game Push Fight, generalized to an arbitrary board and number of pieces. We prove that the game is PSPACE-hard to decide who will win from a given position, even for simple (almost rectangular) hole-free boards. We also analyze the mate-in-1 problem: can the player win in a single turn? One turn in Push Fight consists of up to two "moves" followed by a mandatory "push". With these rules, or generalizing the number of allowed moves to any constant, we show mate-in-1 can be solved in polynomial time. If, however, the number of moves per turn is part of the input, the problem becomes NP-complete. On the other hand, without any limit on the number of moves per turn, the problem becomes polynomially solvable again.

BibTeX - Entry

  author =	{Jeffrey Bosboom and Erik D. Demaine and Mikhail Rudoy},
  title =	{{Computational Complexity of Generalized Push Fight}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Hiro Ito and Stefano Leonardi and Linda Pagli and Giuseppe Prencipe},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-88029},
  doi =		{10.4230/LIPIcs.FUN.2018.11},
  annote =	{Keywords: board games, hardness, mate-in-one}

Keywords: board games, hardness, mate-in-one
Collection: 9th International Conference on Fun with Algorithms (FUN 2018)
Issue Date: 2018
Date of publication: 04.06.2018

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