Artificial Intelligence - Special issue on knowledge representation
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM Journal on Computing
Combining qualitative and quantitative constraints in temporal reasoning
Artificial Intelligence
The complexity of query evaluation in indefinite temporal constraint databases
Selected papers from the international workshop on Uncertainty in databases and deductive systems
On the algebraic structure of combinatorial problems
Theoretical Computer Science
A unifying approach to temporal constraint reasoning
Artificial Intelligence
Temporal reasoning with qualitative and quantitative information about points and durations
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Journal of the ACM (JACM)
On the complexity of integer programming
Journal of the ACM (JACM)
Building tractable disjunctive constraints
Journal of the ACM (JACM)
Tractable disjunctions of linear constraints: basic results and applications to temporal reasoning
Theoretical Computer Science
Introduction to constraint databases
Introduction to constraint databases
A general framework for time granularity and its application to temporal reasoning
Annals of Mathematics and Artificial Intelligence
Temporal representation and reasoning in artificial intelligence: Issues and approaches
Annals of Mathematics and Artificial Intelligence
Constrained Properties, Semilinear Systems, and Petri Nets
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
Constraint Satisfaction Problems on Intervals and Lengths
SIAM Journal on Discrete Mathematics
Handbook of Temporal Reasoning in Artificial Intelligence (Foundations of Artificial Intelligence (Elsevier))
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Complexity of Clausal Constraints Over Chains
Theory of Computing Systems
Decision procedures for bit-vectors, arrays and integers
Decision procedures for bit-vectors, arrays and integers
Non-dichotomies in Constraint Satisfaction Complexity
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Integer programming with 2-variable equations and 1-variable inequalities
Information Processing Letters
Reasoning on interval and point-based disjunctive metric constraints in temporal contexts
Journal of Artificial Intelligence Research
The complexity of temporal constraint satisfaction problems
Journal of the ACM (JACM)
Distance constraint satisfaction problems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Discrete-time temporal reasoning with horn DLRs
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Journal of Logic and Computation
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Temporal reasoning problems arise in many areas of AI, including planning, natural language understanding, and reasoning about physical systems. The computational complexity of continuous-time temporal constraint reasoning is fairly well understood. There are, however, many different cases where discrete time must be considered; various scheduling problems and reasoning about sampled physical systems are two examples. Here, the complexity of temporal reasoning is not as well-studied nor as well-understood. In order to get a better understanding, we consider the powerful Horn disjunctive linear relations (Horn DLR) formalism adapted for discrete time and study its computational complexity. We show that the full formalism is NP-hard and identify several maximal tractable subclasses. We also 'lift' the maximality results to obtain hardness results for other families of constraints. Finally, we discuss how the results and techniques presented in this paper can be used for studying even more expressive classes of temporal constraints.