Temporal Reasoning in Nested Temporal Networks with Alternatives
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.
KeywordsFeasible Solution Temporal Constraint Output Label Temporal Network Base Graph
Unable to display preview. Download preview PDF.
- 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.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.Beck, J.C., Fox, M.S.: Scheduling Alternative Activities. In: Proceedings of AAAI 1999, pp. 680–687. AAAI Press, Menlo Park (1999)Google Scholar
- 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.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.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.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.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.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.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