Document Zbl 07940175

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Comput. Sci.</a> <a href="/?q=in%3A520303" title="Articles in this Issue">1020, Article ID 114924, 18 p. (2024)</a>. </div> <div class="abstract">Summary: In this paper, we give a family of online algorithms for the classical coloring problem of intersection graphs of disks with bounded diameter. Our algorithms make use of a geometric representation of such graphs and are inspired by an algorithm of Fiala et al., but have better competitive ratios. The improvement comes from using two techniques of partitioning the set of vertices before coloring them. One of them is an application of a $b$-fold coloring of the plane. The method is more general and we show how it can be applied to coloring other shapes on the plane as well as adjust it for online $L(2, 1)$-labeling.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68Qxx" title="MSC2020">68Qxx</a> </td> <td class="space"> Theory of computing </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Adisk+graphs">disk graphs</a>; <a href="/?q=ut%3Aonline+coloring">online coloring</a>; <a href="/?q=ut%3Aonline+%5C%28L%282%2C+1%29%5C%29-labeling">online $L(2, 1)$-labeling</a>; <a href="/?q=ut%3Aonline+coloring+geometric+shapes">online coloring geometric shapes</a>; <a href="/?q=ut%3Agraph+coloring">graph coloring</a>; <a href="/?q=ut%3A%5C%28L%282%2C+1%29%5C%29-labeling">$L(2, 1)$-labeling</a>; <a href="/?q=ut%3Adisk+intersection+graphs">disk intersection graphs</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 07940175" data-ciurl="/ci/07940175" data-biburl="/bibtex/07940175.bib" data-amsurl="/amsrefs/07940175.bib" data-xmlurl="/xml/07940175.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07940175.pdf" title="Zbl 07940175 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.tcs.2024.114924" aria-label="DOI for “Online coloring of disk graphs”" title="10.1016/j.tcs.2024.114924">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2206.14564"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">Bodlaender, H. 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