Computational Optimization and Applications

, Volume 51, Issue 3, pp 1211–1229 | Cite as

A combinatorial optimization algorithm for solving the branchwidth problem



In this paper, we consider the problem of computing an optimal branch decomposition of a graph. Branch decompositions and branchwidth were introduced by Robertson and Seymour in their series of papers that proved the Graph Minors Theorem. Branch decompositions have proven to be useful in solving many NP-hard problems, such as the traveling salesman, independent set, and ring routing problems, by means of combinatorial algorithms that operate on branch decompositions. We develop an implicit enumeration algorithm for the optimal branch decomposition problem and examine its performance on a set of classical graph instances.


Branch decomposition Branchwidth Implicit enumeration Partitioning 


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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Industrial & Systems EngineeringUniversity of FloridaGainesvilleUSA
  2. 2.MathematicsHouston Community CollegeHoustonUSA
  3. 3.Computational & Applied MathematicsRice UniversityHoustonUSA

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