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The Computer Journal Advance Access published online on July 19, 2007
The Computer Journal, doi:10.1093/comjnl/bxm037
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© The Author 2007. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Combinatorial Optimization on Graphs of Bounded Treewidth

Hans L. Bodlaender1,* and Arie M. C. A. Koster2

1 Institute of Information and Computing Sciences, Utrecht University, PO Box 80.089, 3508 TB Utrecht, the Netherlands
2 Centre for Discrete Mathematics and its Applications (DIMAP), University of Warwick, Coventry CV4 7AL, UK

* Corresponding author: hansb{at}cs.uu.nl

Received 17 March 2006; revised 11 December 2006

There are many graph problems that can be solved in linear or polynomial time with a dynamic programming algorithm when the input graph has bounded treewidth. For combinatorial optimization problems, this is a useful approach for obtaining fixed-parameter tractable algorithms. Starting from trees and series-parallel graphs, we introduce the concepts of treewidth and tree decompositions, and illustrate the technique with the Weighted Independent Set problem as an example. The paper surveys some of the latest developments, putting an emphasis on applicability, on algorithms that exploit tree decompositions, and on algorithms that determine or approximate treewidth and find tree decompositions with optimal or close to optimal treewidth. Directions for further research and suggestions for further reading are also given.

Key Words: bounded treewidth • paramaterized algorithms


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