Encyclopedia of Algorithms

Editors: Ming-Yang Kao

Automated Search Tree Generation

2004; Gramm, Guo, Hüffner, Niedermeier
  • Falk Hüffner
DOI: https://doi.org/10.1007/978-0-387-30162-4_44

Keywords and Synonyms

Automated proofs of upper bounds on the running time of splitting algorithms    

Problem Definition

This problem is concerned with the automated development and analysis of search tree algorithms. Search tree algorithms are a popular way to find optimal solutions to NP-complete problems.1 The idea is to recursively solve several smaller instances in such a way that at least one branch is a yes-instance if and only if the original instance is. Typically, this is done by trying all possibilities to contribute to a solution certificate for a small part of the input, yielding a small local modification of the instance in each branch.

For example, consider the NP-complete Cluster Editing problem: can a given graph be modified by adding or deleting up to k edges such that the resulting graph is a cluster graph, that is, a graph that is a disjoint union of cliques? To give a search tree algorithm for Cluster Editing, one can use the fact that cluster graphs are exactly...

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Notes

Acknowledgments

Partially supported by the Deutsche Forschungsgemeinschaft, Emmy Noether research group PIAF (fixed‐parameter algorithms), NI 369/4.

Recommended Reading

  1. 1.
    Eppstein, D.: Quasiconvex analysis of backtracking algorithms. In: Proc. 15th SODA, ACM/SIAM, pp. 788–797 (2004)Google Scholar
  2. 2.
    Fedin, S.S., Kulikov, A.S.: Automated proofs of upper bounds on the running time of splitting algorithms. J. Math. Sci. 134, 2383–2391 (2006). Improved results at http://logic.pdmi.ras.ru/~kulikov/autoproofs.html MathSciNetGoogle Scholar
  3. 3.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39, 321–347 (2004)MathSciNetGoogle Scholar
  4. 4.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: Exact algorithms for clique generation. Theor. Comput. Syst. 38, 373–392 (2005)Google Scholar
  5. 5.
    Hüffner, F.: Graph Modification Problems and Automated Search Tree Generation. Diplomarbeit, Wilhelm‐Schickard‐Institut für Informatik, Universität Tübingen (2003)Google Scholar
  6. 6.
    Skjernaa, B.: Exact Algorithms for Variants of Satisfiability and Colouring Problems. Ph. D. thesis, University of Aarhus, Department of Computer Science (2004)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Falk Hüffner
    • 1
  1. 1.Department of Math and Computer ScienceUniversity of JenaJenaGermany