Optimizing tree decompositions in MSO
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...
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| Vydané v: | Logical methods in computer science Ročník 18, Issue 1 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Logical Methods in Computer Science e.V
03.02.2022
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| Predmet: | |
| ISSN: | 1860-5974, 1860-5974 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | 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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| ISSN: | 1860-5974 1860-5974 |
| DOI: | 10.46298/lmcs-18(1:26)2022 |