Document Zbl 1451.60080

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Comput.</a> <a href="/?q=in%3A430061" title="Articles in this Issue">32, No. 1, 59-68 (2019)</a>. </div> <div class="abstract"><div class="pre">Summary: We study the following synchronous process that we call <span class="zbmathjax-textit">repeated balls-into-bins</span>. The process is started by assigning $n$ balls to $n$ bins in an arbitrary fashion. In every subsequent round, one ball is extracted from each non-empty bin according to some fixed strategy (random, FIFO, etc), and re-assigned to one of the $n$ bins uniformly at random. We define a configuration <span class="zbmathjax-textit">legitimate</span> if its maximum load is $\mathcal {O}(\log n)$. We prove that, starting from any configuration, the process converges to a legitimate configuration in linear time and then only takes on legitimate configurations over a period of length bounded by <span class="zbmathjax-textit">any</span> polynomial in $n$, <span class="zbmathjax-textit">with high probability</span> (w.h.p.). This implies that the process is self-stabilizing and that every ball traverses all bins within $\mathcal {O}(n\log ^2 n)$ rounds, w.h.p.</div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7040100">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A7040100">Cited in <strong>6</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A60J10" title="MSC2020">60J10</a> </td> <td class="space"> Markov chains (discrete-time Markov processes on discrete state spaces) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68W20" title="MSC2020">68W20</a> </td> <td class="space"> Randomized algorithms </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aballs+into+bins">balls into bins</a>; <a href="/?q=ut%3Aself-stabilizing+systems">self-stabilizing systems</a>; <a href="/?q=ut%3AMarkov+chains">Markov chains</a>; <a href="/?q=ut%3Aparallel+resource+assignment">parallel resource assignment</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 1451.60080" data-ciurl="/ci/07040100" data-biburl="/bibtex/07040100.bib" data-amsurl="/amsrefs/07040100.bib" data-xmlurl="/xml/07040100.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07040100.pdf" title="Zbl 1451.60080 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/10.1007/s00446-017-0320-4" aria-label="DOI for “Self-stabilizing repeated balls-into-bins”" title="10.1007/s00446-017-0320-4">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1501.04822" title="Note: arXiv document may differ from published version">arXiv</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> <img tabindex="0" src="/static/img/unlock_up.svg" class="cc-license-icon" title="Open version available"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Anagnostopoulos, A., Kirsch, A., Upfal, E.: Load balancing in arbitrary network topologies with stochastic adversarial input. SIAM J. Comput. 34(3), 616-639 (2005) · <a href="/1075.68005" class="nowrap">Zbl 1075.68005</a> · <a href="https://doi.org/10.1137/S0097539703437831" class="nowrap">doi:10.1137/S0097539703437831</a></td> </tr><tr> <td>[2]</td> <td class="space">Berenbrink, P., Friedetzky, T., Goldberg, L.A.: The natural work-stealing algorithm is stable. SIAM J. Comput. 32(5), 1260-1279 (2003) · <a href="/1027.60082" class="nowrap">Zbl 1027.60082</a> · <a href="https://doi.org/10.1137/S0097539701399551" class="nowrap">doi:10.1137/S0097539701399551</a></td> </tr><tr> <td>[3]</td> <td class="space">Dijkstra, E.W.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643-644 (1974) · <a href="/0305.68048" class="nowrap">Zbl 0305.68048</a> · <a href="https://doi.org/10.1145/361179.361202" class="nowrap">doi:10.1145/361179.361202</a></td> </tr><tr> <td>[4]</td> <td class="space">Dolev, S.: Self-Stabilization. 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