Recognizing circle graphs in polynomial time
Journal of the ACM (JACM)
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Mapping the genome: some combinatorial problems arising in molecular biology
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Complexity and algorithms for reasoning about time: a graph-theoretic approach
Journal of the ACM (JACM)
Regular Article: On the Complexity of DNA Physical Mapping
Advances in Applied Mathematics
Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra
Journal of the ACM (JACM)
Simple linear time recognition of unit interval graphs
Information Processing Letters
Journal of Algorithms
Satisfiability problems on intervals and unit intervals
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
On the algebraic structure of combinatorial problems
Theoretical Computer Science
A unifying approach to temporal constraint reasoning
Artificial Intelligence
Maintaining knowledge about temporal intervals
Communications of the ACM
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Tractable disjunctions of linear constraints: basic results and applications to temporal reasoning
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Realizing Interval Graphs with Size and Distance Constraints
SIAM Journal on Discrete Mathematics
The Complexity of Minimal Satisfiability Problems
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Some Observations on Durations, Scheduling and Allen's Algebra
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
A Simple Test for Interval Graphs
WG '92 Proceedings of the 18th International Workshop on Graph-Theoretic Concepts in Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Reasoning about temporal relations : the tractable subalgebras of Allen''''s interval algebra
Reasoning about temporal relations : the tractable subalgebras of Allen''''s interval algebra
Eight maximal tractable subclasses of Allen's algebra with metric time
Journal of Artificial Intelligence Research
Reasoning about temporal relations: The tractable subalgebras of Allen's interval algebra
Journal of the ACM (JACM)
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We study interval-valued constraint satisfaction problems (CSPs), in which the aim is to find an assignment of intervals to a given set of variables subject to constraints on the relative positions of intervals. One interesting question concerning such problems is to determine exactly how the complexity of an interval-valued CSP depends on the set of constraints allowed in instances. For the framework known as Allen's interval algebra this question was completely answered earlier by the authors.Here we extend the qualitative framework of Allen's algebra with additional constraints on the lengths of intervals. We allow these length constraints to be expressed as Horn disjunctive linear relations, a well-known tractable and sufficiently expressive form of constraints. We completely characterize sets of qualitative relations for which the constraint satisfaction problem augmented with arbitrary length constraints of the above form is tractable. We also show that all the remaining cases are NP-complete.