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Intervalizing k-colored graphs

  • Algorithms I
  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 944))

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Abstract

The problem to determine whether a given k-colored graph is a subgraph of a properly k-colored interval graph is shown to be solvable in O(n) time when k = 2, solvable in O(n 2) time when k = 3, and to be NP-complete for any fixed k ≥ 4. This problem has an application in DNA physical mapping. Our algorithm for k = 3 is based on an extensive analysis of the precise structure of graphs of pathwidth two, dynamic programming on certain parts of the input graph, and a careful combination of the results for the different parts.

This research was partially supported by the Foundation for Computer Science (S.I.O.N) of the Netherlands Organization for Scientific Research (N.W.O.) and partially by the ESPRIT Basic Research Actions of the EC under contract 7141 (project ALCOM II).

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References

  1. H. L. Bodlaender, M. R. Fellows, and M. Hallett. Beyond NP-completeness for problems of bounded width: Hardness for the W hierarchy. In Proceedings of the 26th Annual Symposium on Theory of Computing, pages 449–458, New York, 1994. ACM Press.

    Google Scholar 

  2. H. L. Bodlaender, M. R. Fellows, and T. J. Warnow. Two strikes against perfect phylogeny. In Proceedings 19th International Colloquium on Automata, Languages and Programming, pages 273–283, Berlin, 1992. Springer Verlag, Lecture Notes in Computer Science, vol. 623.

    Google Scholar 

  3. H. L. Bodlaender and T. Kloks. A simple linear time algorithm for triangulating three-colored graphs. J. Algorithms, 15:160–172, 1993.

    Google Scholar 

  4. J. A. Ellis, I. H. Sudborough, and J. Turner. The vertex separation and search number of a graph. Information and Computation, 113:50–79, 1994.

    Google Scholar 

  5. M. R. Fellows, M. T. Halett, and H. T. Wareham. DNA physical mapping: Three ways difficult (extended abstract). In T. Lengauer, editor, Proceedings 1st Annual European Symposium on Algorithms ESA '93, pages 157–168. Springer Verlag, Lecture Notes in Computer Science, vol. 726, 1993.

    Google Scholar 

  6. M. C. Golumbic, H. Kaplan, and R. Shamir. On the complexity of dna physical mapping. Advances in Applied Mathematics, 15:251–261, 1994.

    Google Scholar 

  7. R. Idury and A. Schaffer. Triangulating three-colored graphs in linear time and linear space. SIAM J. Disc. Meth., 2:289–293, 1993.

    Google Scholar 

  8. S. Kannan and T. Warnow. Triangulating 3-colored graphs. SIAM J. Disc. Meth., 5:249–258, 1992.

    Google Scholar 

  9. H. Kaplan and R. Shamir. Pathwidth, bandwidth and completion problems to proper interval graphs with small cliques. Technical Report 285/93, Inst. for Computer Science, Tel Aviv University, Tel Aviv, Israel, 1993. To appear in SIAM J. Comput.

    Google Scholar 

  10. H. Kaplan, R. Shamir, and R. E. Tarjan. Tractability of parameterized completion problems on chordal and interval graphs: Minimum fill-in and physical mapping. In Proceedings of the 35th annual symposium on Foundations of Computer Science (FOCS), pages 780–791. IEEE Computer Science Press, 1994.

    Google Scholar 

  11. F. R. McMorris, T. Warnow, and T. Wimer. Triangulating vertex-colored graphs. SIAM J. Disc. Meth., 7(2):296–306, 1994.

    Google Scholar 

  12. R. H. Möhring. Graph problems related to gate matrix layout and PLA folding. In E. Mayr, H. Noltemeier, and M. Sysło, editors, Computational Graph Theory, Comuting Suppl. 7, pages 17–51. Springer Verlag, 1990.

    Google Scholar 

  13. S.-I. Nakano, T. Oguma, and T. Nishizeki. A linear time algorithm for c-triangulating three-colored graphs. Trans. Institute of Electronics, Information and Communication, Eng., A., 377-A(3):543–546, 1994. In Japanese.

    Google Scholar 

  14. J. B. Saxe. Dynamic programming algorithms for recognizing small-bandwidth graphs in polynomial time. SIAM J. Alg. Disc. Meth., 1:363–369, 1980.

    Google Scholar 

  15. M. Steel. The complexity of reconstructing trees from qualitative characters and subtrees. J. of Classification, 9:91–116, 1992.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Utrecht University, P.O. Box 80.089, 3508, TB Utrecht, The Netherlands

    Hans L. Bodlaender & Babette de Fluiter

Authors
  1. Hans L. Bodlaender
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  2. Babette de Fluiter
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Editor information

Zoltán Fülöp Ferenc Gécseg

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© 1995 Springer-Verlag Berlin Heidelberg

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Bodlaender, H.L., de Fluiter, B. (1995). Intervalizing k-colored graphs. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_65

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  • DOI: https://doi.org/10.1007/3-540-60084-1_65

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60084-8

  • Online ISBN: 978-3-540-49425-6

  • eBook Packages: Springer Book Archive

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