Document Zbl 1416.05271

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Graph Algorithms Appl.</a> <a href="/?q=in%3A427999" title="Articles in this Issue">23, No. 2, 345-369 (2019)</a>. </div> <div class="abstract">A geometric graph in the plane is called angle-monotone of width $\alpha$ if any pair of its vertices can be connected by a path such that the angles of any two edges in the path differ by at most $\alpha$.<br class="zbmathjax-paragraph">Main results of this paper are: <br class="zbmathjax-paragraph">1.) Given $S$, a set of points in the plane, there is an angle monotone graph spanning $S$ of width $90^{\circ}$ and with $\mathcal{O}\left(\frac{n^2\log \log n}{\log n}\right)$ edges. <br class="zbmathjax-paragraph">2.) For any point set of size $n$ and any angle $0<\alpha < 45^\circ$, an algorithm is provided for the construction of an angle monotone graph of width $90^\circ + \alpha$ and with $\mathcal O \left(\frac{n}{\alpha}\right)$ edges. <br class="zbmathjax-paragraph">3.) The paper describes a $2$-local routing algorithm of routing ratio $1/\cos\left(45^\circ + \frac{\alpha}{2}\right)$ that finds angle monotone graphs of width $90^\circ + \alpha$ in any $k$-layer 3-sweep graph $H_k$, where $\alpha = 180^\circ/k$. <br class="zbmathjax-paragraph">4.) There is a $1$-local routing algorithm that finds angle-monotone paths of width $120^\circ$ in any full $\Theta_6$-graph.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A6357">Stelian Mihalas (Timişoara)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7058665">Cited in <strong>5</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%3A05C38" title="MSC2020">05C38</a> </td> <td class="space"> Paths and cycles </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C62" title="MSC2020">05C62</a> </td> <td class="space"> Graph representations (geometric and intersection representations, etc.) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aangle+monotone+graph">angle monotone graph</a>; <a href="/?q=ut%3Arouting+ratio">routing ratio</a>; <a href="/?q=ut%3Ageometric+graph">geometric graph</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 1416.05271" data-ciurl="/ci/07058665" data-biburl="/bibtex/07058665.bib" data-amsurl="/amsrefs/07058665.bib" data-xmlurl="/xml/07058665.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07058665.pdf" title="Zbl 1416.05271 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/10.7155/jgaa.00494" aria-label="DOI for “Construction and local routing for angle-monotone graphs”" title="10.7155/jgaa.00494">DOI</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">S. 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