### Some polynomially solvable cases of the inverse ordered 1-median problem on trees

Kien Nguyen
<span title="">2017</span> <i title="National Library of Serbia"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5h57vchldreh5kwnkzol2rss4m" style="color: black;">Filomat</a> </i> &nbsp;
We consider the problem of modifying the edge lengths of a tree at minimum cost such that a prespecified vertex become an ordered 1-median of the perturbed tree. We call this problem the inverse ordered 1-median problem on trees. Gassner showed in 2012 that the inverse ordered 1-median problem on trees is, in general, NP-hard. We, however, address some situations, where the corresponding inverse 1-median problem is polynomially solvable. For the problem on paths with n vertices, we develop an
more &raquo; ... n 3 ) algorithm based on a greedy technique. Furthermore, we prove the NP-hardness of the inverse ordered 1median problem on star graphs and propose a quadratic algorithm that solves the inverse ordered 1-median problem on unweighted stars.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/fil1712651n">doi:10.2298/fil1712651n</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/562lobykpvdvtdgej6xahh33gi">fatcat:562lobykpvdvtdgej6xahh33gi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220424031301/http://www.doiserbia.nb.rs/img/doi/0354-5180/2017/0354-51801712651N.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/bf/39/bf3976bdb0f7d11d42d5610b6a9acc712c022037.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2298/fil1712651n"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>