Document Zbl 1333.05282

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Comput.</a> <a href="/?q=in%3A354082" title="Articles in this Issue">45, No. 2, 317-378 (2016)</a>. </div> <div class="abstract">Summary: We give an algorithm that for an input $n$-vertex graph $G$ and integer $k>0$, in time $2^{O(k)} n$, either outputs that the treewidth of $G$ is larger than $k$, or gives a tree decomposition of $G$ of width at most $5k+4$. This is the first algorithm providing a constant factor approximation for treewidth which runs in time single exponential in $k$ and linear in $n$. Treewidth-based computations are subroutines of numerous algorithms. Our algorithm can be used to speed up many such algorithms to work in time which is single exponential in the treewidth and linear in the input size.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A6566956">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A6566956">Cited in <strong>135</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C85" title="MSC2020">05C85</a> </td> <td class="space"> Graph algorithms (graph-theoretic aspects) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C05" title="MSC2020">05C05</a> </td> <td class="space"> Trees </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68R10" title="MSC2020">68R10</a> </td> <td class="space"> Graph theory (including graph drawing) in computer science </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68W25" title="MSC2020">68W25</a> </td> <td class="space"> Approximation algorithms </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aalgorithms">algorithms</a>; <a href="/?q=ut%3Agraphs">graphs</a>; <a href="/?q=ut%3Atreewidth">treewidth</a>; <a href="/?q=ut%3Aapproximation">approximation</a>; <a href="/?q=ut%3Afixed+parameter+tractability">fixed parameter tractability</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1333.05282" data-ciurl="/ci/06566956" data-biburl="/bibtex/06566956.bib" data-amsurl="/amsrefs/06566956.bib" data-xmlurl="/xml/06566956.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06566956.pdf" title="Zbl 1333.05282 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1137/130947374" aria-label="DOI for “A $c^k n$ 5-approximation algorithm for treewidth”" title="10.1137/130947374">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1304.6321"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">I. 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