Skip to main content
SpringerLink
Log in

Games, Puzzles and Treewidth

  • Chapter
  • First Online:
Treewidth, Kernels, and Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12160))

  • 807 Accesses

Abstract

We discuss some results on the complexity of games and puzzles. In particular, we focus on the relationship between bounded treewidth and the (in-)tractability of games and puzzles in which graphs play a role. We discuss some general methods which are good starting points for finding complexity proofs for games and puzzles.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Unless .

  2. 2.

    E.g., a formula of the form \(\exists _{x_1}\forall _{x_2}\exists _{x_3}\cdots \forall _{x_n} \phi (x_1,x_2,\ldots ,x_n)\), where \(\phi \) is an unquantified boolean formula over binary variables \(x_1,\ldots ,x_n\).

  3. 3.

    A pressure plate, as opposed to a button, is a game element that the player cannot avoid triggering if traversed.

References

  1. Aloupis, G., Demaine, E.D., Guo, A., Viglietta, G.: Classic nintendo games are (NP-)hard. arXiv preprint arXiv:1203.1895 (2012)

  2. Aloupis, G., Demaine, E.D., Guo, A., Viglietta, G.: Classic nintendo games are (computationally) hard. Theoret. Comput. Sci. 586, 135–160 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bodlaender, H.L.: Complexity of path-forming games. Theoret. Comput. Sci. 110(1), 215–245 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bodlaender, H.L., Nederlof, J., van der Zanden, T.C.: Subexponential time algorithms for embedding \({H}\)-minor free graphs. In: Chatzigiannakis, I., Mitzenmacher, M., Rabani, Y., Sangiorgi, D. (eds.) 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016), Leibniz International Proceedings in Informatics (LIPIcs), Dagstuhl, Germany, vol. 55, pp. 9:1–9:14 (2016). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik

    Google Scholar 

  5. Bodlaender, H.L., van der Zanden, T.C.: Improved lower bounds for graph embedding problems. In: Fotakis, D., Pagourtzis, A., Paschos, V.T. (eds.) CIAC 2017. LNCS, vol. 10236, pp. 92–103. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57586-5_9

    Chapter  Google Scholar 

  6. Bodlaender, H.L., van der Zanden, T.C.: On the exact complexity of polyomino packing. In: Ito, H., Leonardi, S., Pagli, L., Prencipe, G. (eds.) 9th International Conference on Fun with Algorithms (FUN 2018), Leibniz International Proceedings in Informatics (LIPIcs), Dagstuhl, Germany, vol. 100, pp. 9:1–9:10 (2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik

    Google Scholar 

  7. Culberson, J.C.: Sokoban is PSPACE-complete. In: Lodi, E., Pagli, L., Santoro, N. (eds.) International Conference on Fun with Algorithms (FUN 1998), pp. 65–76. Carleton Scientific, Waterloo (1998)

    Google Scholar 

  8. Demaine, E.D., Demaine, M.L.: Jigsaw puzzles, edge matching, and polyomino packing: connections and complexity. Graph. Comb. 23(1), 195–208 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Demaine, E.D., Lockhart, J., Lynch, J.: The computational complexity of portal and other 3D video games. In: Ito, H., Leonardi, S., Pagli, L., Prencipe, G. (eds.) 9th International Conference on Fun with Algorithms (FUN 2018), Leibniz International Proceedings in Informatics (LIPIcs), Dagstuhl, Germany, vol. 100, pp. 19:1–19:22 (2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik

    Google Scholar 

  10. Flake, G.W., Baum, E.B.: Rush Hour is PSPACE-complete, or “Why you should generously tip parking lot attendants”. Theoret. Comput. Sci. 270(1–2), 895–911 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Forišek, M.: Computational complexity of two-dimensional platform games. In: Boldi, P., Gargano, L. (eds.) FUN 2010. LNCS, vol. 6099, pp. 214–227. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13122-6_22

    Chapter  Google Scholar 

  12. Fraenkel, A.S., Lichtenstein, D.: Computing a perfect strategy for n \(\times \) n chess requires time exponential in n. J. Comb. Theory, Ser. A 31(2), 199–214 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hearn, R.A., Demaine, E.D.: Games, Puzzles, and Computation. AK Peters/CRC Press, Natick (2009)

    Book  MATH  Google Scholar 

  14. Hodgson, T.J.: A combined approach to the pallet loading problem. AIIE Trans. 14(3), 175–182 (1982)

    Article  Google Scholar 

  15. Impagliazzo, R., Paturi, R., Zane, F.: Which problems have strongly exponential complexity? J. Comput. Syst. Sci. 63, 512–530 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Clarke, D.: DX Interactive. Bloxorz. https://damienclarke.me/#bloxorz

  17. Ito, T., et al.: On the complexity of reconfiguration problems. Theoret. Comput. Sci. 412(12), 1054–1065 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Iwata, S., Kasai, T.: The othello game on an n \(\times \) n board is PSPACE-complete. Theoret. Comput. Sci. 123(2), 329–340 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  19. Pilz, A.: Planar 3-SAT with a clause/variable cycle. arXiv preprint arXiv:1710.07476 (2017)

  20. Robson, J.M.: The complexity of Go. In: 9th World Computer Congress on Information Processing, pp. 413–417 (1983)

    Google Scholar 

  21. Schaefer, T.J.: On the complexity of some two-person perfect-information games. J. Comput. Syst. Sci. 16(2), 185–225 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  22. Uehara, R., Iwata, S.: Generalized Hi-Q is NP-complete. IEICE Trans. (1976-1990) 73(2), 270–273 (1990)

    Google Scholar 

  23. van der Zanden, T.C.: Parameterized complexity of graph constraint logic. In: Husfeldt, T., Kanj, I. (eds.) 10th International Symposium on Parameterized and Exact Computation (IPEC 2015), Leibniz International Proceedings in Informatics (LIPIcs), Dagstuhl, Germany, vol. 43, pp. 282–293 (2015). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik

    Google Scholar 

  24. van der Zanden, T.C., Bodlaender, H.L.: PSPACE-completeness of bloxorz and of games with 2-buttons. In: Paschos, V.T., Widmayer, P. (eds.) CIAC 2015. LNCS, vol. 9079, pp. 403–415. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-18173-8_30

    Chapter  MATH  Google Scholar 

  25. Viglietta, G.: Gaming is a hard job, but someone has to do it!. Theory Comput. Syst. 54(4), 595–621 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  26. Wrochna, M.: Reconfiguration in bounded bandwidth and tree-depth. J. Comput. Syst. Sci. 93, 1–10 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  27. Yato, T., Seta, T.: Complexity and completeness of finding another solution and its application to puzzles. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 86(5), 1052–1060 (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Data Analytics and Digitalisation, Maastricht University, Maastricht, The Netherlands

    Tom C. van der Zanden

Authors
  1. Tom C. van der Zanden
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tom C. van der Zanden .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Fedor V. Fomin

  2. Humboldt-University, Berlin, Germany

    Stefan Kratsch

  3. Utrecht University, Utrecht, The Netherlands

    Erik Jan van Leeuwen

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

van der Zanden, T.C. (2020). Games, Puzzles and Treewidth. In: Fomin, F.V., Kratsch, S., van Leeuwen, E.J. (eds) Treewidth, Kernels, and Algorithms. Lecture Notes in Computer Science(), vol 12160. Springer, Cham. https://doi.org/10.1007/978-3-030-42071-0_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-42071-0_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-42070-3

  • Online ISBN: 978-3-030-42071-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation