An incremental linear-time algorithm for recognizing interval graphs
SIAM Journal on Computing
Recognizing circle graphs in polynomial time
Journal of the ACM (JACM)
Computation structures
Reducing prime graphs and recognizing circle graphs
Combinatorica
A combinatorial approach to temporal reasoning
JCIT Proceedings of the fifth Jerusalem conference on Information technology
Counting endpoint sequences for interval orders and interval graphs
Discrete Mathematics - Special issue on combinatorics and algorithms
Maintaining knowledge about temporal intervals
Communications of the ACM
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Approximation algorithms for temporal reasoning
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Journal of Computer and System Sciences
Planning temporal events using point-interval logic
Mathematical and Computer Modelling: An International Journal
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Interval consistency problems deal with events, each of which is assumed to be an interval on the real line or on any other linearly ordered set. This paper deals with problems in reasoning about such intervals when the precise topological relationships between them is unknown or only partially specified. This work unifies notions of interval algebras for temporal reasoning in artificial intelligence with those of interval orders and interval graphs in combinatorics, obtaining new algorithmic and complexity results of interest to both disciplines. Several versions of the satisjiability, minimum labeling and all consistent solutions problems for temporal (interval) data are investigated. The satisfiability question is shown to be NP-complete even when restricting the possible interval relationships to subsets of the relations intersection and precedence only. On the other hand, we give efficient algorithm for several other restrictions of the problem. Many of these problems are also important in molecular biology, archaeology, and resolving mutual-exclusion constraints in circuit design.