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Treewidth, Tree Decompositions, and Brambles

  1. Arie M.C.A. Koster

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0923

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Koster, A. M. 2011. Treewidth, Tree Decompositions, and Brambles. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. RWTH Aachen University, Lehrstuhl II für Mathematik, Aachen, Germany

Publication History

  1. Published Online: 15 FEB 2011

Abstract

The notions of tree decomposition and treewidth play an important role in the design and analysis of algorithms for combinatorial optimization problems. The notion of a bramble can be used to find a lower bound on the treewidth of a graph. In this article we review the most important results for treewidth, tree decompositions, and brambles, both from a theoretical and practical point of view.

Keywords:

  • treewidth;
  • tree decomposition;
  • fixed parameter complexity;
  • bramble;
  • tree decomposition–based algorithm;
  • pathwidth;
  • branchwidth