Document Zbl 1253.68161

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Comput.</a> <a href="/?q=in%3A304915" title="Articles in this Issue">217, 1-11 (2012)</a>. </div> <div class="abstract">Summary: We show that, for $k$ constant, $k$-tree isomorphism can be decided in logarithmic space by giving an $\mathcal O(k \log n)$ space canonical labeling algorithm. The algorithm computes a unique tree decomposition, uses colors to fully encode the structure of the original graph in the decomposition tree and invokes Lindell’s tree canonization algorithm. As a consequence, the isomorphism, the automorphism, as well as the canonization problem for $k$-trees are all complete for deterministic logspace. Completeness for logspace holds even for simple structural properties of $k$-trees. We also show that a variant of our canonical labeling algorithm runs in time $\mathcal O ((k + 1)!n)$, where n is the number of vertices, yielding the fastest known FPT algorithm for $k$-tree isomorphism.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6092977">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68Q25" title="MSC2020">68Q25</a> </td> <td class="space"> Analysis of algorithms and problem complexity </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68Q17" title="MSC2020">68Q17</a> </td> <td class="space"> Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) </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%3A05C60" title="MSC2020">05C60</a> </td> <td class="space"> Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Agraph+isomorphism">graph isomorphism</a>; <a href="/?q=ut%3Agraph+canonization">graph canonization</a>; <a href="/?q=ut%3A%5C%28k%5C%29-trees">$k$-trees</a>; <a href="/?q=ut%3Aspace+complexity">space complexity</a>; <a href="/?q=ut%3Alogspace+completeness">logspace completeness</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 1253.68161" data-ciurl="/ci/06092977" data-biburl="/bibtex/06092977.bib" data-amsurl="/amsrefs/06092977.bib" data-xmlurl="/xml/06092977.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06092977.pdf" title="Zbl 1253.68161 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/10.1016/j.ic.2012.04.002" aria-label="DOI for “The isomorphism problem for $k$-trees is complete for logspace”" title="10.1016/j.ic.2012.04.002">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Aho, A.; Hopcroft, J.; Ullman, J., The Design and Analysis of Computer Algorithms (1974), Addison-Wesley · <a href="/0326.68005" class="nowrap">Zbl 0326.68005</a></td> </tr><tr> <td>[2]</td> <td class="space">Allender, E.; Mahajan, M., The complexity of planarity testing, Inform. and Comput., 139, 117-134 (2004) · <a href="/1072.68045" class="nowrap">Zbl 1072.68045</a></td> </tr><tr> <td>[3]</td> <td class="space">Àlvarez, C.; Jenner, B., A very hard log-space counting class, Theoret. 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