Interval graphs, interval orders and the consistency of temporal events

Martin Charles Golumbic; Ron Shamir

Interval graphs, interval orders and the consistency of temporal events

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

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 language	English
Title of host publication	Theory of Computing and Systems - ISTCS 1992, Israel Symposium, Proceedings
Editors	Danny Dolev, Michael Rodeh, Zvi Galil, Zvi Galil
Publisher	Springer Verlag
Pages	32-42
Number of pages	11
ISBN (Print)	9783540555537
State	Published - 1992
Externally published	Yes
Event	Israel Symposium on the Theory of Computing and Systems, ISTCS 1992 - Haifa, Israel Duration: 27 May 1992 → 28 May 1992

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	601 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Israel Symposium on the Theory of Computing and Systems, ISTCS 1992
Country/Territory	Israel
City	Haifa
Period	27/05/92 → 28/05/92

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Cite this

Golumbic, M. C., & Shamir, R. (1992). Interval graphs, interval orders and the consistency of temporal events. In D. Dolev, M. Rodeh, Z. Galil, & Z. Galil (Eds.), Theory of Computing and Systems - ISTCS 1992, Israel Symposium, Proceedings (pp. 32-42). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 601 LNCS). Springer Verlag.

Golumbic, Martin Charles ; Shamir, Ron. / Interval graphs, interval orders and the consistency of temporal events. Theory of Computing and Systems - ISTCS 1992, Israel Symposium, Proceedings. editor / Danny Dolev ; Michael Rodeh ; Zvi Galil ; Zvi Galil. Springer Verlag, 1992. pp. 32-42 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "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.",

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Golumbic, MC & Shamir, R 1992, Interval graphs, interval orders and the consistency of temporal events. in D Dolev, M Rodeh, Z Galil & Z Galil (eds), Theory of Computing and Systems - ISTCS 1992, Israel Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 601 LNCS, Springer Verlag, pp. 32-42, Israel Symposium on the Theory of Computing and Systems, ISTCS 1992, Haifa, Israel, 27/05/92.

Interval graphs, interval orders and the consistency of temporal events. / Golumbic, Martin Charles; Shamir, Ron.
Theory of Computing and Systems - ISTCS 1992, Israel Symposium, Proceedings. ed. / Danny Dolev; Michael Rodeh; Zvi Galil; Zvi Galil. Springer Verlag, 1992. p. 32-42 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 601 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - 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.

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Golumbic MC, Shamir R. Interval graphs, interval orders and the consistency of temporal events. In Dolev D, Rodeh M, Galil Z, Galil Z, editors, Theory of Computing and Systems - ISTCS 1992, Israel Symposium, Proceedings. Springer Verlag. 1992. p. 32-42. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

Interval graphs, interval orders and the consistency of temporal events

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Bibliographical note

ASJC Scopus subject areas

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Cite this