Computational complexity of relating time points with intervals

Artificial Intelligence

Volumn 109, Issue 1, 1999, Pages 273-295

  Jonsson, Peter ^a   Drakengren, Thomas ^b   Bäckström, Christer ^a  

^a LINKÖPING UNIVERSITY   (Sweden)

^b Laxgatan 4 ^*  (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; PROBLEM SOLVING;

CONSTRAINT SATISFACTION; POINT INTERVAL ALGEBRA; TEMPORAL REASONING;

ARTIFICIAL INTELLIGENCE;

EID: 0033522707     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0004-3702(99)00007-7     Document Type: Article

References (19)

1. J.F. Allen, Maintaining knowledge about temporal intervals, Comm. ACM 26 (11) (1983) 832-843.
2. J.F. Allen, Temporal reasoning and planning, in: J. Allen, H. Kautz, R. Pelavin, J. Tenenberg (Eds.), Reasoning about Plans, Morgan Kaufmann, San Mateo, CA, 1991, pp. 1-67.
3. K. Appel, W. Haken, Every planar map is four colorable, Bull. Amer. Math. Soc. 82 (1976) 711-712.
4. T. Drakengren, P. Jonsson, A complete classification of tractability in Allen's algebra relative to subsets of basic relations, Artificial Intelligence 106 (2) (1998) 205-219.
5. T. Drakengren, P. Jonsson, Eight maximal tractable subclasses of Allen's algebra with metric time, J. Artif. Intell. Res. 7 (1997) 25-45.
6. T. Drakengren, P. Jonsson, Twenty-one large tractable subclasses of Allen's algebra, Artificial Intelligence 93 (1997) 297-319.
7. M. Garey, D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, New York, 1979.
8. M.C. Golumbic, R. Shamir, Complexity and algorithms for reasoning about time: A graph-theoretic approach, J. ACM 40 (5) (1993) 1108-1133.
9. P. Jonsson, C. Bäckström, A unifying approach to temporal constraint reasoning, Artificial Intelligence 102 (1) (1998) 143-155.
10. P. Jonsson, T. Drakengren, C. Bäckström, Tractable subclasses of the point-interval algebra: A complete classification, in: Proceedings 5th International Conference on Principles of Knowledge Representation and Reasoning (KR-96), Cambridge, MA, 1996, pp. 352-363.
11. M. Koubarakis, Tractable disjunctions of linear constraints, in: Proceedings 2nd International Conference on Principles and Practice for Constraint Programming (CP-96), Cambridge, MA, 1996, pp. 297-307.
12. G. Ligozat, "Corner" relations in Allen's algebra, Constraints 3 (2-3) (1998) 165-177.
13. I. Meiri, Combining qualitative and quantitative constraints in temporal reasoning, Artificial Intelligence 87 (1-2) (1996) 343-385.
14. B. Nebel, H.-J. Bürckert, Software for Machine Assisted Analysis of Allen's Interval Algebra, Available from the authors by anonymous ftp from duck.dfki.uni-sb.de as /pub/papers/DFKI-others/ RR-93-11.programs.tar.Z(1993).
15. B. Nebel, H.-J. Bürckert, Reasoning about temporal relations: A maximal tractable subclass of Allen's interval algebra, J. ACM 42 (1) (1995) 43-66.
16. F. Song, R. Cohen, The interpretation of temporal relations in narrative, in: Proceedings AAAI-88, St. Paul, MN, 1988, pp. 745-750.
17. P. van Beek, R. Cohen, Exact and approximate reasoning about temporal relations, Comput. Intell. 6 (3) (1990) 132-144.
18. M.B. Vilain, A system for reasoning about time, in: Proceedings AAAI-82, Pittsburgh, PA, 1982, pp. 197-201.
19. M.B. Vilain, H.A. Kautz, P.G. van Beek, Constraint propagation algorithms for temporal reasoning: A revised report, in: Readings in Qualitative Reasoning about Physical Systems, Morgan Kaufmann, San Mateo, CA, 1989, pp. 373-381 .