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Practical algorithms for branch-decompositions of planar graphs. (English) Zbl 1326.05035
Summary: Branch-decompositions of graphs have important algorithmic applications. A graph $$G$$ of small branchwidth admits efficient algorithms for many NP-hard problems in $$G$$. These algorithms usually run in exponential time in the branchwidth and polynomial time in the size of $$G$$. It is critical to compute the branchwidth and a branch-decomposition of small width for a given graph in practical applications of these algorithms. It is known that given a planar graph $$G$$ and an integer $$\beta$$, whether the branchwidth of $$G$$ is at most $$\beta$$ can be decided in $$O(n^2)$$ time, and an optimal branch-decomposition of $$G$$ can be computed in $$O(n^3)$$ time. In this paper, we report the practical performance of the algorithms for computing the branchwidth/branch-decomposition of planar $$G$$ and the heuristics for improving the algorithms.

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C85 Graph algorithms (graph-theoretic aspects) 68W40 Analysis of algorithms
LEDA; TSPLIB
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