Optimizing Tree Decompositions in MSO

Authors Mikolaj Bojanczyk, Michal Pilipczuk

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Mikolaj Bojanczyk
Michal Pilipczuk

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Mikolaj Bojanczyk and Michal Pilipczuk. Optimizing Tree Decompositions in MSO. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 15:1-15:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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.
  • tree decomposition
  • treewidth
  • transduction
  • monadic second-order logic


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