Document Zbl 1529.68207

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P.</a>; <a href="/authors/de-kroon.jari-j-h" title="Author Profile">de Kroon, Jari J. H.</a></div> <h2 class="title"> <strong>Finding $k$-secluded trees faster.</strong> <i>(English)</i> <a class="label nowrap" href="/1529.68207">Zbl 1529.68207</a> </h2> <div class="source"> <a href="/serials/483" title="Journal Profile">J. Comput. Syst. Sci.</a> <a href="/?q=in%3A501364" title="Articles in this Issue">138, Article ID 103461, 17 p. (2023)</a>. </div> <div class="abstract">Summary: We revisit the $k$-<span class="zbmathjax-textsc">Secluded Tree</span> problem. Given a vertex-weighted undirected graph $G$, its objective is to find a maximum-weight induced subtree $T$ whose open neighborhood has size at most $k$. We present a fixed-parameter tractable algorithm that solves the problem in time $2^{\mathcal{O} (k\log k)} \cdot n^{\mathcal{O} (1)}$, improving on a double-exponential running time from earlier work by Golovach, Heggernes, Lima, and Montealegre [<a href="/1443.68129">Zbl 1443.68129</a>; <a href="/1443.68130">Zbl 1443.68130</a>]. Starting from a single vertex, our algorithm grows a $k$-secluded tree by branching on vertices in the open neighborhood of the current tree $T$. To bound the branching depth, we prove a structural result that can be used to identify a vertex that belongs to the neighborhood of any $k$-secluded supertree $T^{\prime} \supseteq T$ once the open neighborhood of $T$ becomes sufficiently large. We extend the algorithm to enumerate compact descriptions of all maximum-weight $k$-secluded trees, which allows us to count them as well.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7730240">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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%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%3A68Q27" title="MSC2020">68Q27</a> </td> <td class="space"> Parameterized complexity, tractability and kernelization </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asecluded+tree">secluded tree</a>; <a href="/?q=ut%3AFPT">FPT</a>; <a href="/?q=ut%3Aenumeration+algorithm">enumeration algorithm</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1443.68129">Zbl 1443.68129</a>; <a href="/1443.68130">Zbl 1443.68130</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 1529.68207" data-ciurl="/ci/07730240" data-biburl="/bibtex/07730240.bib" data-amsurl="/amsrefs/07730240.bib" data-xmlurl="/xml/07730240.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07730240.pdf" title="Zbl 1529.68207 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.jcss.2023.05.006" aria-label="DOI for “Finding $k$-secluded trees faster”" title="10.1016/j.jcss.2023.05.006">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2206.09884"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">van Bevern, René; Fluschnik, Till; Mertzios, George B.; Molter, Hendrik; Sorge, Manuel; Suchý, Ondrej, The parameterized complexity of finding secluded solutions to some classical optimization problems on graphs, Discrete Optim., 30, 20-50 (2018) · <a href="/1454.90104" class="nowrap">Zbl 1454.90104</a></td> </tr><tr> <td>[2]</td> <td class="space">van Bevern, René; Fluschnik, Till; Tsidulko, Oxana Yu., Parameterized algorithms and data reduction for the short secluded s-t-path problem, Networks, 75, 1, 34-63 (2020) · <a href="/1533.68116" class="nowrap">Zbl 1533.68116</a></td> </tr><tr> <td>[3]</td> <td class="space">Chechik, Shiri; Johnson, Matthew P.; Parter, Merav; Peleg, David, Secluded connectivity problems, Algorithmica, 79, 3, 708-741 (2017) · <a href="/1380.68307" class="nowrap">Zbl 1380.68307</a></td> </tr><tr> <td>[4]</td> <td class="space">Cygan, Marek; Fomin, Fedor V.; Kowalik, Lukasz; Lokshtanov, Daniel; Marx, Dániel; Pilipczuk, Marcin; Pilipczuk, Michal; Saurabh, Saket, Parameterized Algorithms (2015), Springer · <a href="/1334.90001" class="nowrap">Zbl 1334.90001</a></td> </tr><tr> <td>[5]</td> <td class="space">Downey, Rodney G.; Fellows, Michael R., Parameterized Complexity, Monographs in Computer Science (1999), Springer · <a href="/0961.68533" class="nowrap">Zbl 0961.68533</a></td> </tr><tr> <td>[6]</td> <td class="space">Till, Fluschnik, Elements of Efficient Data Reduction: Fractals, Diminishers, Weights and Neighborhoods (2020), Technische Universität Berlin, PhD thesis · <a href="/1551.68008" class="nowrap">Zbl 1551.68008</a></td> </tr><tr> <td>[7]</td> <td class="space">Fomin, Fedor V.; Golovach, Petr A.; Karpov, Nikolay; Kulikov, Alexander S., Parameterized complexity of secluded connectivity problems, Theory Comput. Syst., 61, 3, 795-819 (2017) · <a href="/1378.68075" class="nowrap">Zbl 1378.68075</a></td> </tr><tr> <td>[8]</td> <td class="space">Fomin, Fedor V.; Golovach, Petr A.; Korhonen, Janne H., On the parameterized complexity of cutting a few vertices from a graph, (Chatterjee, Krishnendu; Sgall, Jirí, Proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science. Proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013. Proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science. Proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, Lecture Notes in Computer Science, vol. 8087 (2013), Springer), 421-432 · <a href="/1398.68231" class="nowrap">Zbl 1398.68231</a></td> </tr><tr> <td>[9]</td> <td class="space">Golovach, Petr A.; Heggernes, Pinar; Lima, Paloma T.; Montealegre, Pedro, Finding connected secluded subgraphs (2017), CoRR · <a href="/1443.68129" class="nowrap">Zbl 1443.68129</a></td> </tr><tr> <td>[10]</td> <td class="space">Golovach, Petr A.; Heggernes, Pinar; Lima, Paloma T.; Montealegre, Pedro, Finding connected secluded subgraphs, J. Comput. Syst. Sci., 113, 101-124 (2020) · <a href="/1443.68130" class="nowrap">Zbl 1443.68130</a></td> </tr><tr> <td>[11]</td> <td class="space">Guo, Jiong; Gramm, Jens; Hüffner, Falk; Niedermeier, Rolf; Wernicke, Sebastian, Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization, J. Comput. Syst. Sci., 72, 8, 1386-1396 (2006) · <a href="/1119.68134" class="nowrap">Zbl 1119.68134</a></td> </tr><tr> <td>[12]</td> <td class="space">Kneis, Joachim; Langer, Alexander; Rossmanith, Peter, A new algorithm for finding trees with many leaves, Algorithmica, 61, 4, 882-897 (2011) · <a href="/1230.68112" class="nowrap">Zbl 1230.68112</a></td> </tr><tr> <td>[13]</td> <td class="space">Luckow, Max-Jonathan; Fluschnik, Till, On the computational complexity of length- and neighborhood-constrained path problems, Inf. Process. Lett., 156, Article 105913 pp. (2020) · <a href="/1478.68251" class="nowrap">Zbl 1478.68251</a></td> </tr><tr> <td>[14]</td> <td class="space">Marx, Dániel, Parameterized graph separation problems, Theor. Comput. Sci., 351, 3, 394-406 (2006) · <a href="/1086.68104" class="nowrap">Zbl 1086.68104</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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