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arXiv · 1701.06937

Optimizing tree decompositions in MSO

Mikołaj Bojańczyk·Michał Pilipczuk
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Abstract

The classic algorithm of Bodlaender and Kloks [J. Algorithms, 1996] solves the following problem in linear fixed-parameter time: given a tree decomposition of a graph of (possibly suboptimal) width k, compute an optimum-width tree decomposition of the graph. In this work, we prove that this problem can also be solved in mso in the following sense: for every positive integer k, there is an mso transduction from tree decompositions of width k to tree decompositions of optimum width. Together with our recent results [LICS 2016], this implies that for every k there exists an mso transduction which inputs a graph of treewidth k, and nondeterministically outputs its tree decomposition of optimum width. We also show that mso transductions can be implemented in linear fixed-parameter time, which enables us to derive the algorithmic result of Bodlaender and Kloks as a corollary of our main result.

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Mikołaj Bojańczyk, Michał Pilipczuk. 2017-01-24. Optimizing tree decompositions in MSO. https://doi.org/10.46298/lmcs-18(1%3A26)2022

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