Pathwidth, bandwidth, and completion problems to proper interval graphs with small cliques

SIAM Journal on Computing

Volumn 25, Issue 3, 1996, Pages 540-561

  Kaplan, Haim ^a   Shamir, Ron ^b  

^a Princeton University   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Bandwidth; Design and analysis of algorithms; Interval graphs; Parameterized complexity; Pathwidth

Indexed keywords

EID: 0037668746     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539793258143     Document Type: Article

References (43)

1. K. ABRAHAMSON, R. DOWNEY, AND M. FELLOWS, Fixed-parameter intractability II, in Proc. 10th Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Comput. Sci. 665, Springer-Verlag, Berlin, 1993, pp. 374-385.
2. S. ARNBORG, D. J. CORNELL, AND A. PROSKUROWSKI, Complexity of finding embedding in a k-tree, SIAM J. Discrete Meth., 8 (1987), pp. 227-284.
3. H. L. BODLAENDER, A linear time algorithm for finding tree-decomposition of small treewidth, in Proc. 25th Symposium on the Theory of Computing, Association for Computing Machinery, New York, 1993, pp. 226-234.
4. H. L. BODLAENDER, M. R. FELLOWS, AND M. T. HALLET, Beyond NP-completeness for problems of bounded width: Hardness for the W hierarchy (extended abstract), in Proc. 26th Symposium on the Theory of Computing, Association for Computing Machinery, New York, 1994, pp. 449-458.
5. H. L. BODLAENDER, M. R. FELLOWS, AND T. J. WARNOW, Two strikes against perfect phylogeny, in Proc. 19th International Comput. Algorithms Lang. Programming, W. Kuich, ed., Lecture Notes in Comput. Sci. 623, Springer-Verlag, Berlin, New York, Heidelberg, 1992, pp. 273-283.
6. H. L. BODLAENDER AND R. H. MÖHRING, The pathwidth and treewidth of cographs, in Proc. 2nd Scandinavian Workshop on Algorithm Theory, 1990, Lecture Notes in Comput. Sci. 447, Springer-Verlag, Berlin, New York, Heidelberg, 1990, pp. 301-309.
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. E. CUTHILL AND J. MCKEE, Reducing the bandwidth of sparse symmetric matrices, in Proc. 24th National Conference of the Association for Computing Machinery, Association for Computing Machinery, New York, 1969, pp. 157-172.
10. X. DENG, P. HELL, AND J. HUANG, Linear-time representation algorithms for proper circulararc graphs and proper interval graphs, Technical Report, School of Computing Science, Simon Fraser University, Burnaby, BC, Canada, 1993; SIAM J. Comput., 25 (1996), pp. 390-403.
11. X. DENG, P. HELL, AND J. HUANG, Linear-time representation algorithms for proper circulararc graphs and proper interval graphs, Technical Report, School of Computing Science, Simon Fraser University, Burnaby, BC, Canada, 1993; SIAM J. Comput., 25 (1996), pp. 390-403.
12. R. G. DOWNEY AND M. R. FELLOWS, Fixed-parameter intractability, in Proc. Structures, IEEE Press, Los Alamitos, CA, 1992, pp. 36-49.
13. _, Fixed-parameter tractability and completeness III: Some structural aspects of the W hierarchy, in Complexity Theory: Current Research (Proc. 1992 Dagstuhl Workshop on Structural Complexity), K. Ambos-Spies, S. Homer, and U. Schöning, eds., Cambridge University Press, Cambridge, UK, 1993, pp. 191-226.
14. M. R. FELLOWS, M. T. HALLET, AND H. T. WAREHAM, DNA physical mapping: Three ways difficult, in Proc. European Symposium on Algorithms (ESA '93), Lecture Notes in Comput. Sci. 726, Springer-Verlag, Berlin, New York, Heidelberg, 1993, pp. 157-168.
15. M. R. FELLOWS AND M. A. LANGSTON, Nonconstructive advances in polynomial time complexity, Inform. Process Lett., 26 (1987), pp. 157-162.
16. _, On well-partial-order theory and its application to combinatorial problems of VLSI design, SIAM J. Discrete Math., 5 (1992), pp. 117-126.
17. M. R. GAREY, R. L. GRAHAM, D. S. JOHNSON, AND D. E. KNUTH, Complexity results for bandwidth minimization. SIAM J. Appl. Math., 34 (1978), pp. 477-495.
18. M. R. GAREY AND D. S. JOHNSON, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, San Francisco, 1979.
19. P. W. GOLDBERG, M. C. GOLUMBIC, H. KAPLAN, AND R. SHAMIR, Four strikes against physical mapping of DNA, J. Comput. Biol., 2 (1995), pp. 139-152.
20. M. C. GOLUMBIC, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
21. M. C. GOLUMBIC, H. KAPLAN, AND R. SHAMIR, Graph sandwich problems, J. Algorithms, 19 (1995), pp. 449-473.
22. _, On the complexity of DNA physical mapping, Adv. Appl. Math., 15 (1994), pp. 251-261.
23. M. C. GOLUMBIC AND R. SHAMIR, Complexity and algorithms for reasoning about time: A graph-theoretic approach, J. Assoc. Comput. Mach., 40 (1993), pp. 1108-1133.
24. E. GURARI AND I. H. SUDBOROUGH, Improved dynamic programming algorithms for the bandwidth minimization and the mincut linear arrangement problem, J. Algorithms, 5 (1984), pp. 531-546.
25. J. GUSTEDT, On the pathwidth of chordal graphs, Technical Report, Fachbereich Mathematik, Technische Universität Berlin, Berlin, Germany, 1992; Discrete Math., to appear.
26. J. GUSTEDT, On the pathwidth of chordal graphs, Technical Report, Fachbereich Mathematik, Technische Universität Berlin, Berlin, Germany, 1992; Discrete Math., to appear.
27. H. KAPLAN, R. SHAMIR, AND R. E. TARJAN, Tractability of parameterized completion problems on chordal and interval graphs: Minimum fill-in and physical mapping (extended abstract), in Proc. 35th Symposium on Foundations of Computer Science, IEEE Press, Los Alamitos, CA, 1994, pp. 780-791.
28. R. M. KARP, Mapping the genome: Some combinatorial problems arising in molecular biology, in Proc. 25th Symposium of the Theory of Computing, Association for Computing Machinery, New York, 1993, pp. 278-285.
29. T. KASHIWABARA AND T. FUJISAWA, An NP-complete problem on interval graphs, in Proc. 12th IEEE Symposium of Circuits and Systems, IEEE Press, Piscataway, NJ, 1979, pp. 82-83.
30. _, NP-completeness of the problem of finding a minimum-clique-number interval graph containing a given graph as a subgraph, in Proc. 12th IEEE Symposium of Circuits and Systems, IEEE Press, Piscataway, NJ, 1979, pp. 657-660.
31. L. M. KIROUSIS AND C. H. PAPADIMITRIOU, Searching and pebbling, Theoret. Comput. Sci., 47 (1986), pp. 205-218.
32. T. KLOKS, Treewidth, Ph.D. thesis, Computer Science Department, Utrecht University, Utrecht, The Netherlands, 1993.
33. Y. KOHARA, K. AKIYAMA, AND K. ISONO, The physical map of the whole E. coli chromosome: Application of a new strategy for rapid analysis and sorting of large genomic libraries, Cell, 50 (1987), pp. 495-508.
34. N. KORTE AND R. H. MÖHRING An incremental linear time algorithm for recognizing interval graphs, SIAM J. Comput., 18 (1989), pp. 68-81.
35. R. H. MÖHRING, Graph problems related to gate matrix layout and PLA folding, in Computational Graph Theory, Computing Supplement 7, G. Tinhofer et al., eds., Springer, Vienna, 1990, pp. 17-51.
36. B. MONIEN, The bandwidth minimization problem for caterpillars with hair length 3 is NP-complete, SIAM J. Algebraic Discrete Meth., 7 (1986), pp. 505-512.
37. B. MONIEN AND I. H. SUDBOROUGH, Min cut is NP-complete for edge weighted trees, Theoret. Comput, Sci., 58 (1988), pp. 209-229.
38. R. NAGARAJA, Current approaches to long-range physical mapping of the human genome, in Techniques for the Analysis of Complex Genomes, R. Anand, ed., Academic Press, London, 1992, pp. 1-18.
39. M. V. OLSON ET AL, Random-clone strategy for genomic restriction mapping in yeast, Proc. Nat. Acad. Sci. U.S.A., 83 (1986), pp. 7826-7830.
40. F. S. ROBERTS, Discrete Mathematical Models, with Applications to Social Biological and Environmental Problems. Prentice-Hall, Englewood Cliffs, NJ, 1976.
41. N. ROBERTSON AND P. D. SEYMOUR, Graph minors I: Excluding a forest, J. Combin. Theory Ser. B, 35 (1983), pp. 39-61.
42. J. B. SAXE, Dynamic programming algorithms for recognizing small-bandwidth graphs in polynomial time, SIAM J. Algebraic Discrete Meth., 1 (1980), pp. 363-369.
43. R. E. TARJAN, Depth-first search and linear graph algorithms, SIAM J. Comput., 1 (1972), pp. 146-160.