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DOI: 10.4230/LIPIcs.STACS.2017.15
URN: urn:nbn:de:0030-drops-70173
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7017/
Bojanczyk, Mikolaj ; Pilipczuk, Michal
Optimizing Tree Decompositions in MSO
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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 Vallée},
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 | |
| Seminar: | 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 06.03.2017 |
