Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T20:54:07.216Z Has data issue: false hasContentIssue false
  • English
  • Français

Efficient variable elimination for semi-structured simple temporal networks with continuous domains

Published online by Cambridge University Press:  01 September 2010

Neil Yorke-Smith  and
Hung H. Bui
Neil Yorke-Smith*
Affiliation:
SRI International, 333 Ravenswood Ave., Menlo Park, CA 94025, USA; e-mail: [email protected], [email protected]
Hung H. Bui*
Affiliation:
SRI International, 333 Ravenswood Ave., Menlo Park, CA 94025, USA; e-mail: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The Simple Temporal Network (STN) is a widely used framework for reasoning about quantitative temporal constraints over variables with continuous or discrete domains. The inference tasks of determining consistency and deriving the minimal network are traditionally achieved by graph algorithms (e.g. Floyd-Warshall, Johnson) or by iteration of narrowing operators (e.g. ΔSTP). None of these methods exploits effectively the tree-decomposition structure of the constraint graph of an STN. Methods based on variable elimination (e.g. adaptive consistency) can exploit this structure, but have not been applied to STNs as far as they could, in part because it is unclear how to efficiently pass the ‘messages’ over continuous domains. We show that for an STN, these messages can be represented compactly as sub-STNs. We then present an efficient message-passing scheme for computing the minimal constraints of an STN. Analysis of this algorithm, Prop-STP, brings formal explanation of the performance of the existing STN solvers ΔSTP and SR-PC. Empirical results validate the efficiency of Prop-STP, demonstrating performance comparable to ΔSTP, in cases where the constraint graph is known to have small tree width, such as those that arise during Hierarchical Task Network planning.

Type
Articles
Information
The Knowledge Engineering Review , Volume 25 , Special Issue 3: Planning and scheduling , September 2010 , pp. 337 - 351
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bliek, C., Sam-Haroud, D. 1999. Path consistency on triangulated constraint graphs. In Proceedings of IJCAI’99, Stockholm, Sweden.Google Scholar
Bresina, J., Jónsson, A. K., Morris, P., Rajan, K. 2005. Activity planning for the Mars exploration rovers. In Proceedings of ICAPS’05, Monterey, CA.Google Scholar
Bui, H. H., Tyson, M., Yorke-Smith, N. 2007. Efficient message passing and propagation of simple temporal constraints. In Proceedings of AAAI 2007 Workshop on Spatial and Temporal Reasoning, Vancouver, Canada.Google Scholar
Bui, H. H., Tyson, M., Yorke-Smith, N. 2008. Efficient message passing and propagation of simple temporal constraints: Results on semi-structured networks. In Proceedings of CP/ICAPS’08 Workshop on Constraint Satisfaction for Planning and Scheduling Problems, Sydney, Australia.Google Scholar
Castillo, L., Fdez-Olivares, J., García-Pérez, F. P. O. 2006. Efficiently handling temporal knowledge in an HTN planner. In Proceedings of ICAPS’06, Cumbria, UK.CrossRefGoogle Scholar
Choueiry, B. Y., Wilson, N. 2006. Personal communication.Google Scholar
Cormen, T., Leiserson, C., Rivest, R. 1990. Introduction to Algorithms. McGraw-Hill.Google Scholar
Dechter, R. 2003. Constraint Processing. Morgan Kaufmann.Google Scholar
Dechter, R., Meiri, I., Pearl, J. 1991. Temporal constraint networks. Artificial Intelligence 49(1–3), 61–95.CrossRefGoogle Scholar
Dechter, R., Pearl, J. 1989. Tree clustering schemes for constraint-processing. Artificial Intelligence 38(3), 353–366.CrossRefGoogle Scholar
Erol, K., Hendler, J., Nau, D. 1994. Semantics for Hierarchical Task-network Planning. Technical report CS-TR-3239. University of Maryland.Google Scholar
Hunsberger, L. 2008. A practical temporal constraint management system for real-time applications. In Proceedings of ECAI’08, Patras, Greece.Google Scholar
Jégou, P., Ndiaye, S., Terrioux, C. 2005. Computing and exploiting tree-decompositions for solving constraint networks. In Proceedings of CP’05, Sitges, Spain.CrossRefGoogle Scholar
Jégou, P., Terrioux, C. 2003. Hybrid backtracking bounded by tree-decomposition of constraint networks. Artificial Intelligence 146(1), 43–75.CrossRefGoogle Scholar
Khatib, L., Morris, P., Morris, R. A., Rossi, F. 2001. Temporal constraint reasoning with preferences. In Proceedings of IJCAI’01, Seattle, WA.Google Scholar
Kjaerulff, U. 1990. Triangulation of Graphs: Algorithms Giving Small Total State Space. Technical report R90-09. Aalborg University.Google Scholar
Laborie, P., Ghallab, M. 1995. Planning with sharable resource constraints. In Proceedings of IJCAI’95, Montréal, Canada.Google Scholar
Larrosa, J., Morancho, E., Niso, D. 2005. On the practical use of variable elimination in constraint optimization problems: ‘still-life’ as a case study. Journal of Artificial Intelligence Research 23, 421–440.CrossRefGoogle Scholar
Myers, K. L., Tyson, M. W., Wolverton, M. J., Jarvis, P. A., Lee, T. J., desJardins, M. 2002. PASSAT: a user-centric planning framework. In Proceedings of the Third Intl. NASA Workshop on Planning and Scheduling for Space, Houston, TX.Google Scholar
Planken, L., de Weerdt, M., van der Krogt, R. 2008. P3C: a new algorithm for the simple temporal problem. In Proceedings of ICAPS’08, Sydney, Australia.Google Scholar
Shi, Y., Lal, A., Choueiry, B. Y. 2004. Evaluating consistency algorithms for temporal metric constraints. In Proceedings of AAAI-04, San Jose, CA.Google Scholar
Smith, D. E., Frank, J., Jónsson, A. K. 2000. Bridging the gap between planning and scheduling. Knowledge Engineering Review 15(1), 47–83.CrossRefGoogle Scholar
Xu, L., Choueiry, B. Y. 2003. A new efficient algorithm for solving the simple temporal problem. In Proceedings of TIME’03, Cairns, Australia.Google Scholar
Yorke-Smith, N. 2005. Exploiting the structure of hierarchical plans in temporal constraint propagation. In Proceedings of AAAI-05, Pittsburgh, PA.Google Scholar