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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
Software:
LEDA; TSPLIB
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