Document Zbl 1477.68199

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SWAT 2018, June 18–20, 2018, Malmö University, Malmö, Sweden. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik. LIPIcs – Leibniz Int. Proc. Inform. 101, Article 9, 14 p. (2018). </div> <div class="abstract">Summary: The <span class="zbmathjax-textsc">Tree Containment</span> problem has many important applications in the study of evolutionary history. Given a phylogenetic network $N$ and a phylogenetic tree $T$ whose leaves are labeled by a set of taxa, it asks if $N$ and $T$ are consistent. While the case of binary $N$ and $T$ has received considerable attention, the more practically relevant variant dealing with biological uncertainty has not. Such uncertainty manifests itself as high-degree vertices (“polytomies”) that are “jokers” in the sense that they are compatible with any binary resolution of their children. Contrasting the binary case, we show that this problem, called <span class="zbmathjax-textsc">Soft Tree Containment</span>, is $\mathcal{NP}$-hard, even if $N$ is a binary, multi-labeled tree in which each taxon occurs at most thrice. On the other hand, we reduce the case that each label occurs at most twice to solving a 2-SAT instance of size $O(|T|^3)$. This implies $\mathcal{NP}$-hardness and polynomial-time solvability on reticulation-visible networks in which the maximum in-degree is bounded by three and two, respectively.<br class="zbmathjax-paragraph">For the entire collection see [<a href="/1390.68019">Zbl 1390.68019</a>].</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7238964">Cited in <strong>4</strong> Documents</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%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%3A92D15" title="MSC2020">92D15</a> </td> <td class="space"> Problems related to evolution </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aphylogenetics">phylogenetics</a>; <a href="/?q=ut%3Areticulation-visible+networks">reticulation-visible networks</a>; <a href="/?q=ut%3Amultifurcating+trees">multifurcating trees</a></div> <div class="software"> <h3>Software:</h3><a href="/software/34266">tcp_package</a>; <a href="/software/12877">Algorithm 447</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 1477.68199" data-ciurl="/ci/07238964" data-biburl="/bibtex/07238964.bib" data-amsurl="/amsrefs/07238964.bib" data-xmlurl="/xml/07238964.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07238964.pdf" title="Zbl 1477.68199 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/10.4230/LIPIcs.SWAT.2018.9" aria-label="DOI for “Tree containment with soft polytomies”" title="10.4230/LIPIcs.SWAT.2018.9">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">Magnus Bordewich and Charles Semple. Reticulation-visible networks. {\it Advances in Applied} {\it Mathematics}, 78:114-141, 2016. · <a href="/1335.05170" class="nowrap">Zbl 1335.05170</a></td> </tr><tr> <td>[2]</td> <td class="space">Joseph Minhow Chan, Gunnar Carlsson, and Raul Rabadan. Topology of viral evolution. {\it Proceedings of the National Academy of Sciences}, 110(46):18566-18571, 2013. · <a href="/1292.92014" class="nowrap">Zbl 1292.92014</a></td> </tr><tr> <td>[3]</td> <td class="space">Richard Cole, Martin Farach-Colton, Ramesh Hariharan, Teresa Przytycka, and Mikkel Thorup. An {\it O}({\it n }log {\it n}) algorithm for the maximum agreement subtree problem for binary trees. {\it SIAM Journal on Computing}, 30(5):1385-1404, 2000. · <a href="/0976.68081" class="nowrap">Zbl 0976.68081</a></td> </tr><tr> <td>[4]</td> <td class="space">A Dress, Katharina Huber, J Koolen, Vincent Moulton, and A Spillner. {\it Basic Phylogenetic} {\it Combinatorics}. Cambridge University Press, 2004.</td> </tr><tr> <td>[5]</td> <td class="space">Jittat Fakcharoenphol, Tanee Kumpijit, and Attakorn Putwattana. A faster algorithm for the tree containment problem for binary nearly stable phylogenetic networks. In {\it 12th In-} {\it ternational Joint Conference on Computer Science and Software Engineering (JCSSE’15)}, pages 337-342. IEEE, 2015.</td> </tr><tr> <td>[6]</td> <td class="space">Philippe Gambette, Andreas D. M. Gunawan, Anthony Labarre, Stéphane Vialette, and Louxin Zhang. Locating a tree in a phylogenetic network in quadratic time. In {\it Proceed-} {\it ings of the 19th Annual International Conference on Research in Computational Molecular} {\it Biology (RECOMB’15)}, volume 9029 of {\it LNCS}, pages 96-107. Springer, 2015. · <a href="/1355.92075" class="nowrap">Zbl 1355.92075</a></td> </tr><tr> <td>[7]</td> <td class="space">Andreas D. M. Gunawan. Solving tree containment problem for reticulation-visible networks with optimal running time. {\it CoRR}, abs/1702.04088, 2017.</td> </tr><tr> <td>[8]</td> <td class="space">Andreas D. M. Gunawan, Bingxin Lu, and Louxin Zhang. A program for verification of phylogenetic network models. {\it Bioinformatics}, 32(17):i503-i510, 2016.</td> </tr><tr> <td>[9]</td> <td class="space">:14</td> </tr><tr> <td>[10]</td> <td class="space">Andreas D. M. Gunawan, Bingxin Lu, and Louxin Zhang. Fast methods for solving the cluster containment problem for phylogenetic networks. {\it CoRR}, 1801.04498, 2018. 5 See [18] for the corresponding reduction.</td> </tr><tr> <td>[11]</td> <td class="space">Andreas D.M. Gunawan, Bhaskar DasGupta, and Louxin Zhang. A decomposition theorem and two algorithms for reticulation-visible networks. {\it Information and Computation}, 252:161-175, 2017. · <a href="/1361.92053" class="nowrap">Zbl 1361.92053</a></td> </tr><tr> <td>[12]</td> <td class="space">Dan Gusfield. {\it ReCombinatorics: the algorithmics of ancestral recombination graphs and} {\it explicit phylogenetic networks}. MIT Press, 2014. · <a href="/1316.92001" class="nowrap">Zbl 1316.92001</a></td> </tr><tr> <td>[13]</td> <td class="space">John Hopcroft and Robert Tarjan. Algorithm 447: Efficient algorithms for graph manipulation. {\it Commun. ACM}, 16(6):372-378, 1973.</td> </tr><tr> <td>[14]</td> <td class="space">Daniel H Huson, Regula Rupp, and Celine Scornavacca. {\it Phylogenetic networks: concepts,} {\it algorithms and applications}. Cambridge University Press, 2010.</td> </tr><tr> <td>[15]</td> <td class="space">Iyad A Kanj, Luay Nakhleh, Cuong Than, and Ge Xia. Seeing the trees and their branches in the network is hard. {\it Theoretical Computer Science}, 401(1-3):153-164, 2008. · <a href="/1147.68059" class="nowrap">Zbl 1147.68059</a></td> </tr><tr> <td>[16]</td> <td class="space">Todd J Treangen and Eduardo PC Rocha. Horizontal transfer, not duplication, drives the expansion of protein families in prokaryotes. {\it PLoS Genet}, 7(1):e1001284, 2011.</td> </tr><tr> <td>[17]</td> <td class="space">René van Bevern, Matthias Mnich, Rolf Niedermeier, and Mathias Weller.Interval scheduling and colorful independent sets.{\it J. Scheduling}, 18(5):449-469, 2015.doi: 10.1007/s10951-014-0398-5. · <a href="/1328.90065" class="nowrap">Zbl 1328.90065</a></td> </tr><tr> <td>[18]</td> <td class="space">Leo Van Iersel, Charles Semple, and Mike Steel. Locating a tree in a phylogenetic network. {\it Information Processing Letters}, 110(23):1037-1043, 2010. · <a href="/1379.68184" class="nowrap">Zbl 1379.68184</a></td> </tr><tr> <td>[19]</td> <td class="space">Mathias Weller. Linear-time tree containment in phylogenetic networks. {\it CoRR}, 1702.06364, 2017.</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. 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