Document Zbl 1508.05122

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Math.</a> <a href="/?q=in%3A493626" title="Articles in this Issue">329, 1-22 (2023)</a>. </div> <div class="abstract">Summary: In this paper, we are interested in the computation of partial hypergraphs whose width is bounded by an integer $k$. Given a hypergraph $H = (V, E)$ the task is to find a “partial” hypergraph $H^\prime = (V, E^\prime)$ (with $E^\prime \subseteq E$) for which the width of its 2-section is at most $k - 1$. Several criteria can be considered for the optimality of the result. The first one is related to the maximum number of hyperedges to include in $H^\prime$ (maximum criteria). Another one is based on the fact that for all $E^{\prime \prime} \subseteq E$ with $E^\prime \subsetneq E^{\prime \prime}$, the width is then strictly greater than $k - 1$ (maximal criteria). Unfortunately, each one of these tasks is NP-hard.<br class="zbmathjax-paragraph">So, as this task can be useful in practice for the processing of graphical models (e.g. constraint networks, cost function networks, Bayesian networks, Markov random fields, …), we propose a polynomial-time algorithm that finds such partial hypergraphs but with no guarantee with respect to optimality. Nevertheless, we show that for an important class of hypergraphs, it can be optimal. Finally, we present experiments performed on a large benchmark containing more than 11,000 instances from different communities. These experiments allow us to evaluate the efficiency of this algorithm from two points of view: first the proximity of the optimality of the result, then its time efficiency in practice.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C65" title="MSC2020">05C65</a> </td> <td class="space"> Hypergraphs </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%3A68R10" title="MSC2020">68R10</a> </td> <td class="space"> Graph theory (including graph drawing) in computer science </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apartial+hypergraph">partial hypergraph</a>; <a href="/?q=ut%3Abounded+treewidth">bounded treewidth</a></div> <div class="software"> <h3>Software:</h3><a href="/software/1620">MiniCon</a>; <a href="/software/43841">HyperBench</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 1508.05122" data-ciurl="/ci/07657081" data-biburl="/bibtex/07657081.bib" data-amsurl="/amsrefs/07657081.bib" data-xmlurl="/xml/07657081.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07657081.pdf" title="Zbl 1508.05122 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.dam.2022.12.025" aria-label="DOI for “Computing partial hypergraphs of bounded width”" title="10.1016/j.dam.2022.12.025">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://hal.science/hal-04361509" title="Open Access at HAL">HAL </a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Arnborg, S.; Corneil, D.; Proskuroswki, A., Complexity of finding embeddings in a k-tree, SIAM J. 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