Document Zbl 07983599

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Comput. Sci.</a> <a href="/?q=in%3A523765" title="Articles in this Issue">1030, Article ID 115047, 13 p. (2025)</a>. </div> <div class="abstract">Summary: We study a graph partition problem where the input is a directed acyclic graph (DAG) representing tasks as vertices and dependencies between tasks as arcs. The goal is to assign the tasks to $k$ heterogeneous machines in a way that minimizes the total energy consumed for completing the tasks. We first show that the problem is <span class="zbmathjax-textsf">NP</span>-hard. Then, we present polynomial-time algorithms for two special cases: one where there are only two machines, and another where the input DAG is a directed path. Finally, we examine a variant where there are only two machines, with one capable of executing a limited number of tasks, and demonstrate that this special case remains computationally hard.</div> <div class="clear"></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%3A05C70" title="MSC2020">05C70</a> </td> <td class="space"> Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68M20" title="MSC2020">68M20</a> </td> <td class="space"> Performance evaluation, queueing, and scheduling in the context of computer systems </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%3A68Q25" title="MSC2020">68Q25</a> </td> <td class="space"> Analysis of algorithms and problem complexity </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A90B35" title="MSC2020">90B35</a> </td> <td class="space"> Deterministic scheduling theory in operations research </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68W40" title="MSC2020">68W40</a> </td> <td class="space"> Analysis of algorithms </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Agraph+partition+problems">graph partition problems</a>; <a href="/?q=ut%3ANP-hardness">NP-hardness</a>; <a href="/?q=ut%3ADAG">DAG</a>; <a href="/?q=ut%3Atask+allocation+problems">task allocation problems</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 07983599" data-ciurl="/ci/07983599" data-biburl="/bibtex/07983599.bib" data-amsurl="/amsrefs/07983599.bib" data-xmlurl="/xml/07983599.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07983599.pdf" title="Zbl 07983599 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.2024.115047" aria-label="DOI for “On the complexity of minimizing energy consumption of partitioning DAG tasks”" title="10.1016/j.tcs.2024.115047">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2404.01022"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">Duan, Y.; Wu, J., Joint optimization of DNN partition and scheduling for mobile cloud computing, (ICPP, 2021), Article 21 pp.</td> </tr><tr> <td>[2]</td> <td class="space">Kwok, Y.-K.; Ahmad, I., Static scheduling algorithms for allocating directed task graphs to multiprocessors, ACM Comput. 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