Realizing interval graphs with size and distance constraints

SIAM Journal on Discrete Mathematics

Volumn 10, Issue 4, 1997, Pages 662-687

  Pe'er, Itsik ^a   Shamir, Ron ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

Computational biology; Distance constraints; Graph algorithms; Interval graphs; NP completeness; Size constraints

Indexed keywords

EID: 4344588372     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480196306373     Document Type: Article

References (37)

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), pp. 832-843.
3. J. F. ALLEN, Reasoning about Plans, Morgan Kaufman, San Mateo, CA, 1991.
4. P. BALDY AND M. MORVAN, A linear time and space algorithm to recognize interval orders, Discrete Appl. Math., 46 (1993), pp. 173-178.
5. R. BELLMAN, On a routing problem, Quart. Appl. Math., 16 (1958), pp. 87-90.
6. S. BENZER, On the topology of the genetic fine structure, in Proc. Nat. Acad. Sci. USA, 45 (1959), pp. 1607-1620.
7. 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), pp. 335-379.
8. A. V. CARRANO, Establishing the order of human chromosome-specific DNA fragments, in Biotechnology and the Human Genome, A. D. Woodhead and B. J. Barnhart, eds., Plenum Press, New York, 1988, pp. 37-50.
9. C. H. COOMBS AND J. E. K. SMITH, On the detection of structures in attitudes and developmental processes, Psych. Rev., 80 (1973), pp. 337-351.
10. X. DENG, P. HELL, AND J. HUANG, Linear Time Representation Algorithms for Proper Circular Arc Graphs and Proper Interval Graphs, Technical report, School of Computing Science, Simon Eraser University, B.C., Canada, 1993.
11. P. FISHBURN, Interval Orders and Interval Graphs, Wiley, New York, 1985.
12. P. FISHBURN AND R. L. GRAHAM, Classes of interval graphs under expanding length restrictions, J. Graph Theory, 9 (1985), pp. 459-472.
13. H. GABOW AND R. E. TARJAN, Faster scaling algorithms for network problems, SIAM J. Comput., 18 (1989), pp. 1013-1036.
14. P. GÁCS AND L. LOVÁSZ, Khachiyan's algorithm for linear programming, Math. Prog. Study, 14 (1981), pp. 61-68.
15. M. R. GAREY AND D. S. JOHNSON, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Co., San Francisco, CA, 1979.
16. P. C. GILMORE AND A. J. HOFFMAN, A characterization of comparability graphs and of interval graphs, Canad. J. Math., 16 (1964), pp. 539-548.
17. M. C. GOLUMBIC, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
18. M. C. GOLUMBIC, H. KAPLAN, AND R. SHAMIR, Graph sandwich problems, J. Algorithms, 19 (1995), pp. 449-473.
19. M. C. GOLUMBIC AND R. SHAMIR, Complexity and algorithms for reasoning about time: A graph-theoretic approach, J. ACM, 40 (1993), pp. 1108-1133.
20. E. D. GREEN AND P. GREEN, Sequence-tagged site (STS) content mapping of human chromosomes: Theoretical considerations and early experiences, PCR Methods and Applications, 1 (1991), pp. 77-90.
21. E. D. GREEN AND M. V. OLSON, Chromosomal region of the Cystic Fibrosis gene in yeast artificial chromosomes: a model for human genome mapping, Science, 250 (1990), pp. 94-98.
22. G. HAJÖS, Über eine art von graphen, Problem 65, Internat. Math. Nachr., 11 (1957).
23. W-L. Hsu AND T-H MA, Substitution decomposition on chordal graphs and applications, in Proc. 2nd Int. Symp. on Algorithms (ISA '91), W L. Hsu and R. C. T. Lee, eds., Lecture Notes in Comput. Sci. 557, Springer-Verlag, New York, 1991, pp. 52-60.
24. G. ISAAK, Discrete interval graphs with bounded representation, Discrete Appl. Math., 33 (1993), pp. 157-183.
25. R. M. KARP, Mapping the genome: Some combinatorial problems arising in molecular biology, in Proc. 25th Annual ACM Symposium on the Theory of Computing, ACM Press, New York, 1993, pp. 278-285.
26. D. G. KENDALL, Incidence matrices, interval graphs, and seriation in archaeology, Pacific J. Math., 28 (1969), pp. 565-570.
27. N. KORTE AND R. H. MÖHRING, Transitive orientation of graphs with side constraints, in Proc. of the International Workshop on Graphtheoretic concepts in Computer Science (WG '85), H. Noltemeier, ed., Universitätsverlag Rudolf Trauner, Linz, 1985, pp. 143-160.
28. N. KORTE AND R. H. MÖHRING, An incremental linear time algorithm for recognizing interval graphs, SIAM J. Comput., 18 (1989), pp. 68-81.
29. K. NÖKEL, Temporally Distributed Symptoms in Technical Diagnosis, Lecture Notes in Artificial Intelligence 517, Springer-Verlag, New York, 1991.
30. J. B. ORLIN AND R. K. AHUJA, New scaling algorithms for the assignment and minimum cycle mean problems, Math. Programming, 54 (1992), pp. 41-56.
31. C. PAPADIMITRIOU AND M. YANNAKAKIS, Scheduling interval ordered tasks, SIAM J. Comput., 8 (1979), pp. 405-409.
32. I. PE'ER AND R. SHAMIR, Satisfiability problems on intervals and unit intervals, Theoret. Comput. Sci., 175 (1997), pp. 349-372.
33. F. S. ROBERTS, Discrete Mathematical Models, with Applications to Social, Biological and Environmental Problems, Prentice-Hall, Englewood Cliffs, NJ, 1976.
34. L. N. SHEVRIN AND N. D. FILIPPOV, Partially ordered sets and their comparability graphs, Siberian Math. J., 11 (1970), pp. 497-509.
35. R. STANLEY, Hyperplane arrangements, interval orders, and trees, Proc. Nat. Acad. Sci., 93 (1996), pp. 2620-2625.
36. S. A. WARD AND R. H. HALSTEAD, Computation Structures, MIT Press, Cambridge, MA, 1990.
37. A. B. WEBBER, Proof of an Interval Satisfiability Conjecture, Western Illinois University, Macomb, IL, 1994, manuscript.