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STCSP — structured temporal constraint satisfaction problems

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Abstract

Temporal Constraint Satisfaction Problems (TCSP) is a well-known approach for representing and processing temporal knowledge. Important properties of the knowledge can be inferred by computing the minimal networks of TCSPs. Consistency and feasible values are immediately obtained; computing solutions can be assisted. Yet, in general, computing the minimal network of a disjunctive TCSP is intractable. The minimal network approach requires computation of the full network in order to answer a query. In this paper we characterize TCSPs for which subsets of the minimal network can be computed without having to compute the whole network. The partial computation is enabled by decomposition of the problem into a tree of sub-problems that share at most pairs of time points. Such decompositions are termed sim/2-tree decompositions. For TCSPs that have sim/2-tree decompositions, minimal constraints of input propositions can be computed by independent computations of the minimal networks of the sub-problems at most twice. It is also shown that the sim/2-tree characterization is a minimal set of conditions. The sim/2-tree decomposition extends former results about decomposition of a TCSP into bi-connected components. An algorithm for identifying a sim/2-tree decomposition of a TCSP is provided as well. Finally, the sim/2-tree decomposition is generalized in an inductive manner, which enables components of a decomposition to be further decomposed. For that purpose a model of Structured Temporal Constraint Satisfaction Problems (STCSP(n), 0 ⩽ n), where STCSP(0) is simply TCSP, STCSP(1) is a set of STCSP(0)s, and in general, STCSP(n) for 1 ⩽ n is a set of STCSP(n − 1)s, is introduced.

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References

  1. A.V. Aho, J.E. Hopcroft and J.D. Ullman, The Design of Computer Algorithms (Addison-Wesley, Reading, MA, 1975) pp. 200-201.

    Google Scholar 

  2. J.F. Allen, Maintaining knowledge about temporal intervals, Commun. ACM 26(11) (1983) 832-843.

    Article  MATH  Google Scholar 

  3. J.F. Allen, Towards a general theory of action and time, Commun. Artif. Intell. 23(2) (1984) 123-154.

    Article  MATH  Google Scholar 

  4. J.F. Allen and P.J. Hayes, A commonsense theory of time, in: Proc. IJCAI '85 (1985) pp. 528-531.

  5. G. Ariav, A temporally oriented data model, ACM Trans. Database Systems 11(4) (1986).

  6. F. Bacchus, J. Tenenberg and J.A. Koomen, A non-refied temporal logic, Artif. Intell. 52 (1991) 87-108.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Balaban and Y. Kornatzky, A data model for processes based on relative time, J. Intell. Inform. Systems 7(1) (1996) 29-50.

    Article  Google Scholar 

  8. M. Boddy, J. Carciofini and B. Schrag, Managing disjunction for practical temporal reasoning, in: Proc. KR-92 (1992).

  9. J. Clifford and D.S. Warren, Formal semantics for time in databases, ACM Trans. Database Systems 8(2) (1983).

  10. T. Dean, Using temporal hierarchies to efficiently maintain large temporal data base, J. ACM 36(4) (1989) 687-718.

    Article  MATH  MathSciNet  Google Scholar 

  11. T.M. Dean and D.V. McDermott, Temporal data base management, Artif. Intell. 32 (1987) 1-55.

    Article  Google Scholar 

  12. R. Dechter, I. Meiri and J. Pearl, Temporal constraint network, Artif. Intell. 49 (1991) 61-95.

    Article  MATH  MathSciNet  Google Scholar 

  13. R. Dechter and J. Pearl, Network based heuristics for constraint satisfaction problems, Artif. Intell. 34(1) (1988) 1-38.

    Article  MathSciNet  Google Scholar 

  14. R. Dechter and J. Pearl, Tree clustering for constraint networks, Artif. Intell. 38 (1988) 353-366.

    Article  MathSciNet  Google Scholar 

  15. E.C. Freuder, A sufficient condition of backtrack-bounded search, J. ACM 32 (1985) 755-761.

    Article  MATH  MathSciNet  Google Scholar 

  16. M.C. Golumbic and R. Shamir, Complexity and algorithms for reasoning about time: A graph-theoretic approach, J. ACM 40 (1993) 1108-1133.

    Article  MATH  MathSciNet  Google Scholar 

  17. M. Gyssens, P.G. Jeavons and D.A Choen, Decomposition constraint satisfaction problems using data base techniques, Artif. Intell. 66 (1994) 57-89.

    Article  MATH  Google Scholar 

  18. C.S. Jensen, L. Mark and N. Roussopoulos, Incremental implementation model for relational databases with transaction time, IEEE Trans. on Knowledge and Data Engineering (1990).

  19. P. Jonsson and C. Backstrom, A linear-programming approach to temporal reasoning, in: Proc. AAAI-96 (1996) pp. 1235-1240.

  20. H. Kautz and P.B. Ladkin, Integrating metric and qualitative temporal reasoning, in: Proc. AAAI-91 (1991) pp. 241-246.

  21. P.B. Ladkin and A. Reinefeld, Effective solution of qualitative interval constraint problem, Artif. Intell. 57 (1992) 105-124.

    Article  MathSciNet  Google Scholar 

  22. D. McDermott, A temporal logic for reasoning about processes and plans, Cognitive Science 6 (1982) 101-155.

    Article  Google Scholar 

  23. I. Meiri, Combining qualitative and quantitative constraints in temporal reasoning, Artif. Intell. 87(1–2) (1996) 343-385.

    Article  MathSciNet  Google Scholar 

  24. J. Moyne, T. Teorey and L. McAfee, Time sequence ordering extensions to the entity-relationship model and their application to automated manufacturing process, Data & Knowledge Engineering 6 (1991) 421-443.

    Article  Google Scholar 

  25. M. Poesio and R.J. Brachman, Metric constraints for maintaining appointments: Dates and repeated activities, in: Proc. AAAI-91 (1991) 253-259.

  26. T. Rosen, Structured temporal constraints satisfaction problems, M.Sc. dissertation, Ben-Gurion University of the Negev, Beer Sheva, Israel (1995).

    Google Scholar 

  27. E. Schwalb and R. Dechter, Processing disjunctions in temporal constraint networks, Artif. Intell. 93(1–2) (1997) 29-41.

    Article  MATH  MathSciNet  Google Scholar 

  28. Y. Shoham, Reasoning about change: time and causation from the stand point of artificial intelligent, Ph.D. dissertation, Yale University (1986).

  29. P. Van Beek, Reasoning about qualitative temporal information, Artif. Intell. 58 (1992) 297-326.

    Article  MATH  MathSciNet  Google Scholar 

  30. G.T.J. Wuu and U. Dayal, A uniform model for temporal object-oriented databases, Proc. IEEE Data Engineering (1992) 584-593.

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Authors and Affiliations

  1. Information Systems Program, Department of Industrial & Management Engineering, Ben-Gurion University, Beer-Sheva, Israel

    Mira Balaban

  2. Department of Mathematics and Computer Science, Ben-Gurion University, Beer-Sheva, Israel

    Tzachi Rosen

Authors
  1. Mira Balaban
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  2. Tzachi Rosen
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Balaban, M., Rosen, T. STCSP — structured temporal constraint satisfaction problems. Annals of Mathematics and Artificial Intelligence 25, 35–67 (1999). https://doi.org/10.1023/A:1018913618840

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