Search results for "Treewidth"

Optimal Tree Decompositions Revisited: A Simpler Linear-Time FPT Algorithm

2020

In 1996, Bodlaender showed the celebrated result that an optimal tree decomposition of a graph of bounded treewidth can be found in linear time. The algorithm is based on an algorithm of Bodlaender and Kloks that computes an optimal tree decomposition given a non-optimal tree decomposition of bounded width. Both algorithms, in particular the second, are hardly accessible. We present the second algorithm in a much simpler way in this paper and refer to an extended version for the first. In our description of the second algorithm, we start by explaining how all tree decompositions of subtrees defined by the nodes of the given tree decomposition can be enumerated. We group tree decompositions …