eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-03-06
15:1
15:13
10.4230/LIPIcs.STACS.2017.15
article
Optimizing Tree Decompositions in MSO
Bojanczyk, Mikolaj
Pilipczuk, Michal
The classic algorithm of Bodlaender and Kloks 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, 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol066-stacs2017/LIPIcs.STACS.2017.15/LIPIcs.STACS.2017.15.pdf
tree decomposition
treewidth
transduction
monadic second-order logic