License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2017.15
URN: urn:nbn:de:0030-drops-70173
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7017/
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Bojanczyk, Mikolaj ; Pilipczuk, Michal

Optimizing Tree Decompositions in MSO

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LIPIcs-STACS-2017-15.pdf (0.9 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{bojanczyk_et_al:LIPIcs:2017:7017,
  author =	{Mikolaj Bojanczyk and Michal Pilipczuk},
  title =	{{Optimizing Tree Decompositions in MSO}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{15:1--15:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Heribert Vollmer and Brigitte ValleĢe},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7017},
  URN =		{urn:nbn:de:0030-drops-70173},
  doi =		{10.4230/LIPIcs.STACS.2017.15},
  annote =	{Keywords: tree decomposition, treewidth, transduction, monadic second-order logic}
}

Keywords: tree decomposition, treewidth, transduction, monadic second-order logic
Collection: 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Issue Date: 2017
Date of publication: 06.03.2017

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