Nested Precedence Networks with Alternatives: Recognition, Tractability, and Models

  • Roman Barták
  • Ondřej Čepek
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5253)


Integrated modeling of temporal and logical constraints is important for solving real-life planning and scheduling problems. Logical constrains extend the temporal formalism by reasoning about alternative activities in plans/schedules. Temporal Networks with Alternatives (TNA) were proposed to model alternative and parallel processes, however the problem of deciding which activities can be consistently included in such networks is NP-complete. Therefore a tractable subclass of Temporal Networks with Alternatives was proposed. This paper shows formal properties of these networks where precedence constraints are assumed. Namely, an algorithm that effectively recognizes whether a given network belongs to the proposed sub-class is studied and the proof of tractability is given by proposing a constraint model where global consistency is achieved via arc consistency.


temporal networks alternatives constraint models complexity 


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  1. 1.
    Barták, R., Čepek, O.: Temporal Networks with Alternatives: Complexity and Model. In: Proceedings of the Twentieth International Florida AI Research Society Conference (FLAIRS), pp. 641–646. AAAI Press, Menlo Park (2007)Google Scholar
  2. 2.
    Barták, R., Čepek, O.: Nested Temporal Networks with Alternatives: Recognition and Tractability. In: Applied Computing 2008 - Proceedings of 23rd Annual ACM Symposium on Applied Computing, vol. 1, pp. 156–157. ACM, New York (2008)CrossRefGoogle Scholar
  3. 3.
    Barták, R., Čepek, O., Surynek, P.: Discovering Implied Constraints in Precedence Graphs with Alternatives. Annals of Operations Research. Springer, Heidelberg (to appear, 2008)Google Scholar
  4. 4.
    Beck, J.C., Fox, M.S.: Constraint-directed techniques for scheduling alternative activities. Artificial Intelligence 121, 211–250 (2000)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. Journal of the ACM 30, 479–513 (1983)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Horling, B., Leader, V., Vincent, R., Wagner, T., Raja, A., Zhang, S., Decker, K., Harvey, A.: The Taems White Paper, University of Massachusetts (1999),
  7. 7.
    Kim, P., Williams, B., Abramson, M.: Executing Reactive, Model-based Programs through Graph-based Temporal Planning. In: Proceedings of International Joint Conference on Artificial Intelligence (IJCAI), pp. 487–493 (2001)Google Scholar
  8. 8.
    Kuster, J., Jannach, D., Friedrich, G.: Handling Alternative Activities in Resource-Constrained Project Scheduling Problems. In: Proceedings of Twentieth International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 1960–1965 (2007)Google Scholar
  9. 9.
    Nuijten, W., Bousonville, T., Focacci, F., Godard, D., Le Pape, C.: MaScLib: Problem description and test bed design (2003),
  10. 10.
    Tsamardinos, I., Vidal, T., Pollack, M.E.: CTP: A New Constraint-Based Formalism for Conditional Temporal Planning. Constraints 8(4), 365–388 (2003)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Roman Barták
    • 1
  • Ondřej Čepek
    • 1
    • 2
  1. 1.Faculty of Mathematics and PhysicsCharles University in PraguePraha 1Czech Republic
  2. 2.Institute of Finance and AdministrationPraha 10Czech Republic

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