Combinatorica
Graph minors: X. obstructions to tree-decomposition
Journal of Combinatorial Theory Series B
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Constructive Linear Time Algorithms for Branchwidth
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Tour Merging via Branch-Decomposition
INFORMS Journal on Computing
A complete anytime algorithm for treewidth
UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
Planar Branch Decompositions I: The Ratcatcher
INFORMS Journal on Computing
Planar Branch Decompositions II: The Cycle Method
INFORMS Journal on Computing
New upper bounds on the decomposability of planar graphs
Journal of Graph Theory
Computing branchwidth via efficient triangulations and blocks
Discrete Applied Mathematics
Semi-nice tree-decompositions: The best of branchwidth, treewidth and pathwidth with one algorithm
Discrete Applied Mathematics
Treewidth computations I. Upper bounds
Information and Computation
Computing branch decomposition of large planar graphs
WEA'08 Proceedings of the 7th international conference on Experimental algorithms
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
A branch and bound algorithm for exact, upper, and lower bounds on treewidth
AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Optimal branch-decomposition of planar graphs in O(n3) time
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
SOFSEM'05 Proceedings of the 31st international conference on Theory and Practice of Computer Science
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
Width Parameters Beyond Tree-width and their Applications
The Computer Journal
Finding good decompositions for dynamic programming on dense graphs
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
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As many problems can be solved in polynomial time on graphs of bounded branchwidth, there is a need for efficient and practical algorithms that find branch decompositions of small width of given graphs. In this paper, we give the first local search algorithm for this problem. Using non-trivial combinatorial properties of the neighbourhood space, significant reductions in the search space can be obtained. The fitness function can be easily tuned to express the expected cost in the dynamic programming step for specific problems. The algorithm is tested on a number of planar and non-planar graphs. For all tested planar graphs the algorithm found an optimal branch decomposition. For most non-planar graphs, we obtained branch decompositions of width equal to or smaller than the treewidth. Our experiments indicate that local search is a very suitable technique for finding branch decompositions of small width.