TY - GEN
T1 - Interval graphs, interval orders and the consistency of temporal events
AU - Golumbic, Martin Charles
AU - Shamir, Ron
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.
PY - 1992
Y1 - 1992
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=85029767238&partnerID=8YFLogxK
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AN - SCOPUS:85029767238
SN - 9783540555537
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 32
EP - 42
BT - Theory of Computing and Systems - ISTCS 1992, Israel Symposium, Proceedings
A2 - Dolev, Danny
A2 - Rodeh, Michael
A2 - Galil, Zvi
A2 - Galil, Zvi
PB - Springer Verlag
T2 - Israel Symposium on the Theory of Computing and Systems, ISTCS 1992
Y2 - 27 May 1992 through 28 May 1992
ER -