Complexity and algorithms for reasoning about time: a graph-theoretic approach

@article{Golumbic1993ComplexityAA,
  title={Complexity and algorithms for reasoning about time: a graph-theoretic approach},
  author={Martin Charles Golumbic and Ron Shamir},
  journal={J. ACM},
  year={1993},
  volume={40},
  pages={1108-1133}
}
Temporal events are regarded here as intervals on a time line. This paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified. This work unifies notions of interval algebras in artificial intelligence with those of interval orders and interval graphs in combinatorics. The satisfiability, minimal labeling, all solutions, and all realizations problems are considered for temporal (internal) data… 

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References

SHOWING 1-10 OF 48 REFERENCES

Reasoning About Qualitative Temporal Information

  • P. V. Beek
  • Mathematics, Computer Science
    Artif. Intell.
  • 1992

A combinatorial approach to temporal reasoning

  • A. BelferM. Golumbic
  • Computer Science, Mathematics
    Proceedings of the 5th Jerusalem Conference on Information Technology, 1990. 'Next Decade in Information Technology'
  • 1990
It is described how representation structures for counting the number of endpoint sequences associated with a given interval order or interval graph can be used in temporal reasoning. Efficient

Approximation Algorithms for Temporal Reasoning

New approximation algorithms for temporal relations between intervals introduced by James Allen are examined, their effectiveness is examined, and under what conditions the algorithms are exact are determined.

Constraint Propagation Algorithms for Temporal Reasoning

Computing the consequences of temporal assertions is shown to be computationally intractable in the interval-based representation, but not in the point-based one, but a fragment of the interval language can be expressed using the point language and benefits from the tractability of the latter.

Interval graphs and related topics

An Incremental Linear-Time Algorithm for Recognizing Interval Graphs

This paper presents a much simpler algorithm using a related, but much more informative tree representation of interval graphs.

The complexity of satisfiability problems

An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.

Interval graphs and interval orders