Skip to main content
SpringerLink
Log in

Parity Games on Graphs with Medium Tree-Width

  • Conference paper
Mathematical Foundations of Computer Science 2011 (MFCS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6907))

Abstract

This paper studies the problem of solving parity games on graphs with bounded tree-width. Previous work by Obdržálek has produced an algorithm that uses \(n^{O(k^2)}\) time and \(n^{O(k^2)}\) space, where k is the tree-width of the graph that the game is played on. This paper presents an algorithm that uses n O(k logn) time and O(n + k logn) space. This is the fastest known algorithm for parity games whose tree-width k satisfies (in standard asymptotic notation) k ∈ ω(logn) and \(k \in o(\sqrt{n}/\log n)\).

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amir, E.: Efficient approximation for triangulation of minimum treewidth. In: Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence, pp. 7–15. Morgan Kaufmann Publishers Inc., San Francisco (2001)

    Google Scholar 

  2. Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM Journal on Algebraic and Discrete Methods 8(2), 277–284 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bodlaender, H.L.: A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM Journal on Computing 25(6), 1305–1317 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bodlaender, H.L.: Treewidth: Algorithmic techniques and results. In: Privara, I., Ružička, P. (eds.) MFCS 1997. LNCS, vol. 1295, pp. 19–36. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  5. Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)

    Google Scholar 

  6. Emerson, E.A., Jutla, C.S.: Tree automata, mu-calculus and determinacy. In: Proceedings of the 32nd Annual Symposium on Foundations of Computer Science, pp. 368–377. IEEE Computer Society Press, Washington, DC (1991)

    Chapter  Google Scholar 

  7. Emerson, E.A., Jutla, C.S., Sistla, A.P.: On model-checking for fragments of μ-calculus. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 385–396. Springer, Heidelberg (1993)

    Google Scholar 

  8. Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)

    MATH  Google Scholar 

  9. Jurdziński, M.: Deciding the winner in parity games is in UP ∩ co-UP. Information Processing Letters 68(3), 119–124 (1998)

    Article  MathSciNet  Google Scholar 

  10. Jurdziński, M., Paterson, M., Zwick, U.: A deterministic subexponential algorithm for solving parity games. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 117–123. ACM/SIAM (2006)

    Google Scholar 

  11. McNaughton, R.: Infinite games played on finite graphs. Annals of Pure and Applied Logic 65(2), 149–184 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mostowski, A.W.: Games with forbidden positions. Technical Report 78, University of Gdańsk (1991)

    Google Scholar 

  13. Obdržálek, J.: Fast mu-calculus model checking when tree-width is bounded. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 80–92. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  14. Robertson, N., Seymour, P.D.: Graph minors. II. Algorithmic aspects of tree-width. Journal of Algorithms 7(3), 309–322 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  15. Schewe, S.: Solving parity games in big steps. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 449–460. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Stirling, C.: Local model checking games (Extended abstract). In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 1–11. Springer, Heidelberg (1995)

    Google Scholar 

  17. Zielonka, W.: Infinite games on finitely coloured graphs with applications to automata on infinite trees. Theoretical Computer Science 200, 135–183 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, UK

    John Fearnley

  2. Department of Computer Science and Information Systems, University of London, Birkbeck, UK

    Oded Lachish

Authors
  1. John Fearnley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Oded Lachish
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Filip Murlak  & Piotr Sankowski  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag GmbH Berlin Heidelberg

About this paper

Cite this paper

Fearnley, J., Lachish, O. (2011). Parity Games on Graphs with Medium Tree-Width. In: Murlak, F., Sankowski, P. (eds) Mathematical Foundations of Computer Science 2011. MFCS 2011. Lecture Notes in Computer Science, vol 6907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22993-0_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22993-0_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22992-3

  • Online ISBN: 978-3-642-22993-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation