Encyclopedia of Algorithms

2016 Edition
| Editors: Ming-Yang Kao

Automated Search Tree Generation

  • Falk Hüffner
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-2864-4_44

Years and Authors of Summarized Original Work

  • 2004; Gramm, Guo, Hüffner, Niedermeier

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 the graphs that do...

Keywords

Automated proofs of upper bounds on the running time of splitting algorithms 
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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 (2004) Quasiconvex analysis of backtracking algorithms. In: Proceedings of the 15th SODA. ACM/SIAM, pp 788–797Google Scholar
  2. 2.
    Fedin SS, Kulikov AS (2006) Automated proofs of upper bounds on the running time of splitting algorithms. J Math Sci 134:2383–2391. Improved results at http://logic.pdmi.ras.ru/~kulikov/autoproofs.htmlMathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Gramm J, Guo J, Hüffner F, Niedermeier R (2004) Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39:321–347MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Gramm J, Guo J, Hüffner F, Niedermeier R (2005) Graph-modeled data clustering: exact algorithms for clique generation. Theor Comput Syst 38:373– 392zbMATHCrossRefGoogle Scholar
  5. 5.
    Hüffner F (2003) Graph modification problems and automated search tree generation. Diplomarbeit, Wilhelm-Schickard-Institut für Informatik, Universitüt TübingenGoogle Scholar
  6. 6.
    Skjernaa B (2004) Exact algorithms for variants of satisfiability and colouring problems. PhD thesis, Department of Computer Science, University of AarhusGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

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