Automated Generation of Search Tree Algorithms for Graph Modification Problems

  • Jens Gramm
  • Jiong Guo
  • Falk Hüffner
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2832)


We present a (seemingly first) framework for an automated generation of exact search tree algorithms for NP-hard problems. The purpose of our approach is two-fold—rapid development and improved upper bounds. Many search tree algorithms for various problems in the literature are based on complicated case distinctions. Our approach may lead to a much simpler process of developing and analyzing these algorithms. Moreover, using the sheer computing power of machines it may also lead to improved upper bounds on search tree sizes (i.e., faster exact solving algorithms) in comparison with previously developed “hand-made” search trees.


Search Tree Automate Generation Vertex Cover Input Graph Reduction Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Chen, J., Kanj, I.: Improved exact algorithms for MAX-SAT. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 341–355. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Chen, J., Kanj, I., Jia, W.: Vertex cover: further observations and further improvements. Journal of Algorithms 41, 280–301 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Dahllöf, V., Jonsson, P.: An algorithm for counting maximum weighted independent sets and its applications. In: Proc. 13th ACM SODA, pp. 292–298 (2002)Google Scholar
  4. 4.
    Drori, L., Peleg, D.: Faster exact solutions for some NP-hard problems. Theoretical Computer Science 287(2), 473–499 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: fixed-parameter algorithms for clique generation. In: Petreschi, R., Persiano, G., Silvestri, R. (eds.) CIAC 2003. LNCS, vol. 2653, pp. 108–119. Springer, Heidelberg (2003)Google Scholar
  6. 6.
    Hirsch, E.A.: New worst-case upper bounds for SAT. Journal of Automated Reasoning 24(4), 397–420 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Lewis, J.M., Yannakakis, M.: The node-deletion problem for hereditary properties is NP-complete. J. Comp. Sys. Sci. 20(2), 219–230 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    McKay, B.D.: nauty user’s guide (version 1.5). Technical report TR-CS-90-02, Australian National University, Department of Computer Science (1990)Google Scholar
  9. 9.
    Natanzon, A., Shamir, R., Sharan, R.: Complexity classification of some edge modification problems. Discrete Applied Mathematics 113, 109–128 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Niedermeier, R., Rossmanith, P.: An efficient fixed parameter algorithm for 3-Hitting Set. Journal of Discrete Algorithms (2003) (to appear)Google Scholar
  11. 11.
    Niedermeier, R., Rossmanith, P.: On efficient fixed-parameter algorithms for Weighted Vertex Cover. Journal of Algorithms 47(2), 63–77 (2003)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Robson, J.M.: Algorithms for maximum independent sets. Journal of Algorithms 7, 425–440 (1986)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Shamir, R., Sharan, R., Tsur, D.: Cluster graph modification problems. In: Kučera, L. (ed.) WG 2002. LNCS, vol. 2573, pp. 379–390. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jens Gramm
    • 1
  • Jiong Guo
    • 1
  • Falk Hüffner
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany

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