Interval graphs, interval orders and the consistency of temporal events

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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, minimum labeling and all consistent solutions problems are considered for temporal (interval) data. Several versions are investigated by restricting the possible interval relationships yielding different complexity results. We show that even when the temporal data comprises of subsets of relations based on intersection and precedence only, the satisfiability question is NP-Complete. On the positive side, we have obtained efficient algorithms for several restrictions of the problem. In the process, the interval graph sandwich problem is introduced, and is shown to be NP-complete. This problem is also important in molecular biology, where it arises in physical mapping of DNA material.

Original languageEnglish
Title of host publicationTheory of Computing and Systems - ISTCS 1992, Israel Symposium, Proceedings
EditorsDanny Dolev, Michael Rodeh, Zvi Galil, Zvi Galil
PublisherSpringer Verlag
Number of pages11
ISBN (Print)9783540555537
StatePublished - 1992
Externally publishedYes
EventIsrael Symposium on the Theory of Computing and Systems, ISTCS 1992 - Haifa, Israel
Duration: 27 May 199228 May 1992

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume601 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


ConferenceIsrael Symposium on the Theory of Computing and Systems, ISTCS 1992

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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