Complexity classification in qualitative temporal constraint reasoning

We study the computational complexity of the qualitative algebra which is a temporal constraint formalism that combines the point algebra, the point-interval algebra and Allen's interval algebra. We identify all tractable fragments and show that every other fragment is NP-complete.

[1]  Christer Bäckström,et al.  Computational Complexity of Relating Time Points with Intervals , 1999, Artif. Intell..

[2]  Peter Jonsson,et al.  Eight Maximal Tractable Subclasses of Allen's Algebra with Metric Time , 1997, J. Artif. Intell. Res..

[3]  Manolis Koubarakis,et al.  Tractable disjunctions of linear constraints: basic results and applications to temporal reasoning , 2001, Theor. Comput. Sci..

[4]  Ron Shamir,et al.  Complexity and algorithms for reasoning about time: a graph-theoretic approach , 1993, JACM.

[5]  Christer Bäckström,et al.  A Unifying Approach to Temporal Constraint Reasoning , 1998, Artif. Intell..

[6]  Frank Wolter,et al.  Spatio-temporal representation and reasoning based on RCC-8 , 2000, International Conference on Principles of Knowledge Representation and Reasoning.

[7]  Peter Jonsson,et al.  Point algebras for temporal reasoning: Algorithms and complexity , 2003, Artif. Intell..

[8]  Henry A. Kautz,et al.  Constraint propagation algorithms for temporal reasoning: a revised report , 1989 .

[9]  Itay Meiri,et al.  Combining Qualitative and Quantitative Constraints in Temporal Reasoning , 1991, Artif. Intell..

[10]  Abdul Sattar,et al.  A New Framework for Reasoning about Points, Intervals and Durations , 1999, IJCAI.

[11]  Peter Jeavons,et al.  Reasoning about temporal relations: The tractable subalgebras of Allen's interval algebra , 2003, JACM.

[12]  Marc B. Vilain,et al.  A System for Reasoning About Time , 1982, AAAI.

[13]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[14]  Jean-François Condotta,et al.  Computational Complexity of Propositional Linear Temporal Logics Based on Qualitative Spatial or Temporal Reasoning , 2002, FroCoS.

[15]  Robin Hirsch,et al.  Expressive Power and Complexity in Algebraic Logic , 1997, J. Log. Comput..

[16]  Eddie Schwalb,et al.  Temporal Constraints: A Survey , 1998, Constraints.

[17]  Peter Jeavons,et al.  Constraint Satisfaction Problems on Intervals and Length , 2004, SIAM J. Discret. Math..

[18]  Gérard Ligozat.  “Corner” Relations in Allen's algebra , 2004, Constraints.

[19]  Federico Barber,et al.  Reasoning on Interval and Point-based Disjunctive Metric Constraints in Temporal Contexts , 2000, J. Artif. Intell. Res..

[20]  Peter van Beek,et al.  Exact and approximate reasoning about temporal relations 1 , 1990, Comput. Intell..

[21]  Peter Jonsson,et al.  Twenty-One Large Tractable Subclasses of Allen's Algebra , 1997, Artif. Intell..

[22]  Peter Jonsson,et al.  Extending the point algebra into the qualitative algebra , 2002, Proceedings Ninth International Symposium on Temporal Representation and Reasoning.

[23]  Bernhard Nebel,et al.  Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra , 1994, JACM.

[24]  Johan de Kleer,et al.  Readings in qualitative reasoning about physical systems , 1990 .