Satisfiability problems on intervals and unit intervals

Theoretical Computer Science

Volumn 175, Issue 2, 1997, Pages 349-372

  Pe'er, Itsik ^a   Shamir, Ron ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; GRAPH THEORY; PROBLEM SOLVING;

INTERNAL SATISFIABILITY; LINEAR TIME ALGORITHMS;

ALGORITHMS;

EID: 0346046160     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(96)00208-3     Document Type: Article

References (38)

1. R.K. Ahuja, T.A. Magnanti and J.B. Orlin, Network Flows: Theory, Algorithms and Applications (Prentice-Hall, Englewood Cliffs, NJ, 1993).
2. J.F. Allen, Maintaining knowledge about temporal intervals, Comm. ACM 26 (1983) 832-843.
3. J.F. Allen, Reasoning about plans (Morgan Kaufman, Los Altos, CA, 1991).
4. P. Baldy and M. Morvan, A linear time and space algorithm to recognize interval orders, Discrete Appl. Math. 46 (1993) 173-178.
5. S. Benzer, On the topology of the genetic fine structure, Proc. Nat. Acad. Sci. USA 45 (1959) 1607-1620.
6. K.S. Booth and G.S. Lueker, Testing for the consecutive ones property, interval graphs, and planarity using PQ-tree algorithms, J. Comput. System Sci. 13 (1976) 335-379.
7. A.V. Carrano, Establishing the order of human chromosome-specific DNA fragments, in: A.D. Woodhead and B.J. Barnhart, ed., Biotechnology and the Human Genome (Plenum Press, 1988) 37-50.
8. C.H. Coombs and J.E.K. Smith, On the detection of structures in attitudes and developmental processes, Psych. Rev. 80 (1973) 337-351.
9. X. Deng, P. Hell and J. Huang, Linear time representation algorithms for proper circular arc graphs and proper interval graphs, SIAM J. Comput. 25 (1996) 390-403.
10. P. Fishburn, Intransitive indifference with unequal indifference intervals, J. Math. Psych. 7 (1970) 144-149.
11. P. Fishburn, Interval Orders and Interval Graphs (Wiley, New York, 1985).
12. D.R. Fulkerson and O.A. Gross, Incidence matrices and interval graphs, Pacific J. Math. 15 (1965) 835-855.
13. P.C. Gilmore and A.J. Hoffman, A characterization of comparability graphs and of interval graphs, Canad. J. Math. 16 (1964) 539-548.
14. P.W. Goldberg, M.C. Golumbic, H. Kaplan and R. Shamir, Four strikes against physical mapping of DNA, J. Comput. Biology 2 (1) (1995) 139-152.
15. M.C. Golumbic, Interval graphs and related topics, Discrete Math. 55 (1985) 113-121.
16. M.C. Golumbic and R. Shamir, Complexity and algorithms for reasoning about time: A graph-theoretic approach, J. ACM 40 (1993) 1108-1133.
17. G. Hajös, Über eine art von graphen, Intern. Math. Nachr. 11 (1957) problem 65.
18. W.-L. Hsu, A simple test for interval graphs, in: W.-L. Hsu and R.C.T. Lee, eds., Proc. 18th Int. Workshop (WG '92), Graph-Theoretic Concepts in Computer Science, Lecture Notes in Computer Science, Vol. 657 (Springer, Berlin, 1992) 11-16.
19. W.-L. Hsu and T.-H. Ma, Substitution decomposition on chordal graphs and applications, in: W.-L. Hsu and R.C.T. Lee, eds., Proc. 2nd Int. Symp on Algorithms (ISA '91), Lecture Notes in Computer Science, Vol. 557 (Springer, Berlin, 1991) 52-60.
20. H. Kaplan and R. Shamir, Pathwidth, bandwidth and completion problems to proper interval graphs with small cliques, SIAM J. Comput. 25 (1996) 540-561.
21. R.M. Karp, Mapping the genome: some combinatorial problems arising in molecular biology, in: Proc. 25th STOC (ACM Press, New York, 1993) pp. 278-285.
22. D.G. Kendall, Incidence matrices, interval graphs, and seriation in archaeology, Pacific J. Math. 28 (1969) 565-570.
23. D.G. Kendall, Some problems and methods in statistical archaeology, World Archaeol. 1 (1969) 68-76.
24. N. Korte and R.H. Möhring, Transitive orientation of graphs with side constraints, in: H. Noltemeier, ed., Proc. Internat. Workshop on Graph-theoretic concepts in Computer Science (WG '85) Würzburg (Universitätsverlag Rudolf Trauner, Linz, 1985) 143-160.
25. N. Korte and R.H. Möhring, An incremental linear time algorithm for recognizing interval graphs, SIAM J. Comput. 18 (1989) 68-81.
26. P. Lichter et al., High-resolution mapping of human chromosome 11 by in situ hybridization with cosmid clones, Science 247 (1990) 64-69.
27. R.H. Möhring, Algorithmic aspects of comparability graphs and interval graphs, in: I. Rival, ed., Graphs and Order (Reidel, Dordrecht, 1985) 41-101.
28. K. Nökel, Temporally Distributed Symptoms in Technical Diagnosis. Lecture Notes in Artificial Intelligence, Vol. 517. (Springer, Berlin, 1991).
29. J.B. Orlin and R.K. Ahuja, New scaling algorithms for the assignment and minimum cycle mean problems, Math. Programming 54 (1992) 41-56.
30. C. Papadimitriou and M. Yannakakis, Scheduling interval ordered tasks, SIAM J. Comput. 8 (1979) 405-409.
31. F.S. Roberts, Indifference graphs, in: F. Harary, ed., Proof Techniques in Graph Theory (Academic Press, New York, 1969) 139-146.
32. F.S. Roberts, Discrete Mathematical Models, with Applications to Social Biological and Environmental Problems (Prentice-Hall, Englewood Cliffs, NJ, 1976).
33. T.J. Schaefer, The complexity of satisfiability problems, in: Proc. 10th Annual ACM Symp. on Theory of Computing (1978) 216-226.
34. B. Schieber and U. Vishkin, On finding lowest common ancestors: Simplifiction and parallelization, SIAM J. Comput. 17 (1988) 1253-1262.
35. S.A. Ward and R.H. Halstead, Computation Structures (MIT Press, Cambridge, MA, 1990).
36. J.D. Watson, M. Gilman, J. Witkowski and M. Zoller, Recombinant DNA (W.H. Freeman, New York, 2nd ed., 1992).
37. A.B. Webber, Proof of an interval satisfiability conjecture, manuscript, Wesstern Illinois University, 1994.
38. I. Pe'er and R. Shamir, Interval graphs with side (and size) constraints. in: Proc. .3of the Third Annual European Symp. on Algorithms (ESA 95) Corfu. Greece, Lecture Notes in Computer Science, Vol. 979 (Springer, Berlin, 1995) 142-154.