Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Easy problems for tree-decomposable graphs
Journal of Algorithms
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
Random sampling of large planar maps and convex polyhedra
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Constructive Linear Time Algorithms for Branchwidth
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Dominating Sets in Planar Graphs: Branch-Width and Exponential Speed-Up
SIAM Journal on Computing
Planar Branch Decompositions II: The Cycle Method
INFORMS Journal on Computing
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
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
Computational study on planar dominating set problem
Theoretical Computer Science
Computational study for planar connected dominating set problem
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
A local search algorithm for branchwidth
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Computational study on bidimensionality theory based algorithm for longest path problem
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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A graph of small branchwidth admits efficient dynamic programming algorithms for many NP-hard problems on the graph. A key step in these algorithms is to find a branch decomposition of small width for the graph. Given a planar graph G of n vertices, an optimal branch decomposition of G can be computed in polynomial time, e.g., by the edge-contraction method in O(n3) time. All known algorithms for the planar branch decomposition use Seymour and Thomas procedure which, given an integer β, decides whether G has the branchwidth at least β or not in O(n2) time. Recent studies report efficient implementations of Seymour and Thomas procedure that compute the branchwidth of planar graphs of size up to one hundred thousand edges in a practical time and memory space. Using the efficient implementations as a subroutine, it is reported that the edge-contraction method computes an optimal branch decomposition for planar graphs of size up to several thousands edges in a practical time but it is still time consuming for graphs with larger size. In this paper, we propose divide-and-conquer based algorithms of using Seymour and Thomas procedure to compute optimal branch decompositions of planar graphs. Our algorithms have time complexity O(n3). Computational studies show that our algorithms are much faster than the edge-contraction algorithms and can compute an optimal branch decomposition of some planar graphs of size up to 50,000 edges in a practical time.