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Comput. Sci.</a> <a href="/?q=in%3A516210" title="Articles in this Issue">1010, Article ID 114699, 15 p. (2024)</a>. </div> <div class="abstract">Summary: Given an edge-weighted metric complete graph with \(n\) vertices, the maximum weight metric triangle packing problem is to find a set of \(n / 3\) vertex-disjoint triangles with the total weight of all triangles in the packing maximized. Several simple methods can lead to a 2/3-approximation ratio. However, this barrier is not easy to break. Chen et al. proposed a randomized approximation algorithm with an expected ratio of \((0.66768 - \varepsilon)\) for any constant \(\varepsilon > 0\). In this paper, we improve the approximation ratio to \((0.66835 - \varepsilon)\). Furthermore, we can derandomize our algorithm.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7898961">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%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%3Aapproximation+algorithms">approximation algorithms</a>; <a href="/?q=ut%3Ametric">metric</a>; <a href="/?q=ut%3Atriangle+packing">triangle packing</a>; <a href="/?q=ut%3Acycle+packing">cycle packing</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07898961" data-ciurl="/ci/07898961" data-biburl="/bibtex/07898961.bib" data-amsurl="/amsrefs/07898961.bib" data-xmlurl="/xml/07898961.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07898961.pdf" title="Zbl 07898961 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.2024.114699" aria-label="DOI for “A deterministic approximation algorithm for metric triangle packing”" title="10.1016/j.tcs.2024.114699">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">Kirkpatrick, D. 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