Abstract
Our goal is to start the investigation of dynamic algorithms for solving games that are played on finite graphs. The dynamic game determinacy problem calls for finding efficient algorithms that decide the winner of the game when the underlying graph undergoes repeated modifications. In this paper, we focus on turn-based reachability games. We provide an algorithm that solves the dynamic reachability game problem on trees. The amortized time complexity of our algorithm is O(logn), where n is the number of nodes in the current graph.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chatterjee, K., Henzinger, T., Piterman, N.: Algorithms for büchi games. In: Proceedings of the 3rd Workshop of Games in Design and Verification (GDV 2006) (2006)
Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to algorithms, 2nd edn. MIT Press and McGraw-Hill (2001)
Demetrescu, C., Italiano, G.: Fully dynamic transitive closure: Breaking through the O(n 2) barrier. In: Proceedings of FOCS 2000, pp. 381–389 (2000)
Demetrescu, C., Italiano, G.: A new approach to dynamic all pairs shortest paths. In: Proceedings of STOC 2003, pp. 159–166 (2003)
Eppstein, D., Galil, Z., Italiano, G.: Dynamic graph algorithms. In: Atallah, M. (ed.) Algorithms and Theoretical Computing Handbook. CRC Press, Boca Raton (1999)
Grädel, E.: Model checking games. In: Proceedings of WOLLIC 2002. Electronic Notes in Theoretical Computer Science, vol. 67. Elsevier, Amsterdam (2002)
Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)
Immerman, N.: Number of quantifiers is better than number of tape cells. Journal of Computer and System Sciences 22, 384–406 (1981)
King, V.: Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs. In: Proceedings of FOCS 1999, pp. 81–91 (1999)
Kozen, D.: The design and analysis of algorithms. Monographs in computer science. Springer, New York (1992)
Murawski, A.: Reachability games and game semantics: Comparing nondeterministic programs. In: Proceedings of LICS 2008, pp. 353–363 (2008)
Tarjan, R.: Data structures and network algorithms. Regional Conference Series in Applied Mathematics, vol. 44. SIAM, Philadelphia (1983)
Radmacher, F., Thomas, W.: A game theoretic approach to the analysis of dynamic networks. In: Proceedings of the 1st Workshop on Verification of Adaptive Systems, VerAS 2007. Electronic Notes in Theoretical Computer Science, vol. 200(2), pp. 21–37. Kaiserslautern, Germany (2007)
Rodity, L.: A faster and simpler fully dynamic transitive closure. In: Proceedings of SODA 2003, pp. 401–412 (2003)
Roditty, L., Zwick, U.: Improved dynamic reachability algorithm for directed graphs. In: Proceedings of FOCS 2002, pp. 679–689 (2002)
Roditty, L., Zwick, U.: A fully dynamic reachability algorithm for directed graphs with an almost linear update time. In: Proceedings of 36th ACM Symposium on Theory of Computing (STOC 2004), pp. 184–191 (2004)
Thomas, W.: Infinite games and verification (Extended abstract of a tutorial). In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 58–64. Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Khoussainov, B., Liu, J., Khaliq, I. (2009). A Dynamic Algorithm for Reachability Games Played on Trees. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_41
Download citation
DOI: https://doi.org/10.1007/978-3-642-03816-7_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03815-0
Online ISBN: 978-3-642-03816-7
eBook Packages: Computer ScienceComputer Science (R0)