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On the approximation of largest common subtrees and largest common point sets

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Algorithms and Computation (ISAAC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 834))

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Abstract

This paper considers the approximability of the largest common subtree and the largest common subgraph problems, which have applications in molecular biology. It is shown that approximating the problems within a factor of n ε is NP-complete, while a general search algorithm which approximates both problems within a factor of O(n/log n) is presented. Moreover, several variants of the largest common subtree problem are studied.

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References

  1. T. Akutsu. An RNC algorithm for finding a largest common subtree of two trees. IEICE Transactions on Information and Systems, vol. E75-D, no. 1, pp. 95–101, Jan. 1992

    Google Scholar 

  2. T. Akutsu. On determining the congruity of point sets in higher dimensions. These proceedings.

    Google Scholar 

  3. S. Arora, C. Lund, R. Motwani, M. Sudan and M. Szegedy. Proof verification and hardness of approximation problems. Proc. 33rd IEEE Symp. on Foundations of Computer Science, pp. 14–23, Oct. 1992

    Google Scholar 

  4. B. Berger and J. Rompel. A better performance guarantee for approximate graph coloring. Algorithmica, vol. 5, no. 4, pp. 459–466, 1990.

    Article  Google Scholar 

  5. C. Branden and J. Tooze. Introduction to Protein Structure, Garland Publishing Inc., New York, 1991

    Google Scholar 

  6. M. R. Garey and D. S. Johnson. Computers and Intractability, Freeman, New York, 1979

    Google Scholar 

  7. M. M. Halldórsson. A still better performance guarantee for approximate graph coloring. Inform. Process. Lett., vol. 45, pp. 19–23, 25 January 1993.

    Google Scholar 

  8. R. Maier. The complexity of some problems on subsequences and supersequences. J. ACM, vol. 25, pp. 322–336, 1978

    Article  Google Scholar 

  9. C. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes. J. Computer and System. Sciences, vol. 43, no. 3, pp. 425–440, Dec. 1991

    Google Scholar 

  10. R. B. Russel and G. J. Barton. Multiple protein sequence alignment from tertiary structure comparison: assignment of global and residue confidence levels. PROTEINS: Structure, Function, and Genetics, vol. 14, pp. 309–323, 1992

    Google Scholar 

  11. Y. Takahashi, Y. Satoh, H. Suzuki and S. Sasaki. Recognition of largest common structural fragment among a variety of chemical structures. Analytical Sciences, vol. 3, pp.23–28, 1987.

    Google Scholar 

  12. G. Vriend and C Sander. Detection of common three-dimensional substructures in proteins. PROTEINS: Structure, Function, and Genetics, vol. 11, pp. 52–58, 1991

    Google Scholar 

  13. K. Zhang and T. Jiang. Some MAX SNP-hard results concerning unordered labeled trees. To appear in Information Processing Letters.

    Google Scholar 

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Ding-Zhu Du Xiang-Sun Zhang

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© 1994 Springer-Verlag Berlin Heidelberg

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Akutsu, T., Halldórsson, M.M. (1994). On the approximation of largest common subtrees and largest common point sets. In: Du, DZ., Zhang, XS. (eds) Algorithms and Computation. ISAAC 1994. Lecture Notes in Computer Science, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58325-4_205

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  • DOI: https://doi.org/10.1007/3-540-58325-4_205

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58325-7

  • Online ISBN: 978-3-540-48653-4

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