Temporal Reasoning in Nested Temporal Networks with Alternatives

  • Roman Barták
  • Ondřej Čepek
  • Martin Hejna
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5129)

Abstract

Temporal networks play a crucial role in modeling temporal relations in planning and scheduling applications. Temporal Networks with Alternatives (TNAs) were proposed to model alternative and parallel processes in production scheduling, however the problem of deciding which nodes can be consistently included in such networks is NP-complete. A tractable subclass, called Nested TNAs, can still cover a wide range of real-life processes, while the problem of deciding node validity is solvable in polynomial time. In this paper, we show that adding simple temporal constraints (instead of precedence relations) to Nested TNAs makes the problem NP-hard again. We also present several complete and incomplete techniques for temporal reasoning in Nested TNAs.

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References

  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, Papers from the 2007 AAAI Workshop on Spatial and Temporal Reasoning, Technical Report WS-07-12, pp. 1–8. AAAI Press, Menlo Park (2007)Google Scholar
  3. 3.
    Beck, J.C., Fox, M.S.: Scheduling Alternative Activities. In: Proceedings of AAAI 1999, pp. 680–687. AAAI Press, Menlo Park (1999)Google Scholar
  4. 4.
    Blythe, J.: An Overview of Planning Under Uncertainty. AI Magazine 20(2), 37–54 (1999)MathSciNetGoogle Scholar
  5. 5.
    Dechter, R., Meiri, I., Pearl, J.: Temporal Constraint Networks. Artificial Intelligence 49, 61–95 (1991)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, San Francisco (1979)MATHGoogle Scholar
  7. 7.
    Hamadi, Y.: Cycle-cut decomposition and log-based reconciliation. In: ICAPS Workshop on Connecting Planning Theory with Practice, pp. 30–35 (2004)Google Scholar
  8. 8.
    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) (2001)Google Scholar
  9. 9.
    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
  10. 10.
    Laborie, P.: Resource temporal networks: Definition and complexity. In: Proceedings of the 18th International Joint Conference on Artificial Intelligence, pp. 948–953 (2003)Google Scholar
  11. 11.
    Moffitt, M.D., Peintner, B., Pollack, M.E.: Augmenting Disjunctive Temporal Problems with Finite-Domain Constraints. In: Proceedings of the 20th National Conference on Artificial Intelligence (AAAI 2005), pp. 1187–1192. AAAI Press, Menlo Park (2005)Google Scholar
  12. 12.
    Nuijten, W., Bousonville, T., Focacci, F., Godard, D., Le Pape, C.: MaScLib: Problem description and test bed design (2003), http://www2.ilog.com/masclib
  13. 13.
    Stergiou, K., Koubarakis, M.: Backtracking algorithms for disjunctions of temporal constraints. In: Proceedings of the 15th National Conference on Artificial Intelligence (AAAI 1998), pp. 248–253. AAAI Press, Menlo Park (1998)Google Scholar
  14. 14.
    Tsamardinos, Vidal, T., Pollack, M.E.: CTP: A New Constraint-Based Formalism for Conditional Temporal Planning. Constraints 8(4), 365–388 (2003)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Roman Barták
    • 1
  • Ondřej Čepek
    • 1
  • Martin Hejna
    • 1
  1. 1.Faculty of Mathematics and PhysicsCharles University in PraguePraha 1Czech Republic

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