A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit <a rel="external noopener" href="https://users.cs.fiu.edu/~giri/papers/stretch.pdf">the original URL</a>. The file type is <code>application/pdf</code>.
<i title="Society for Industrial & Applied Mathematics (SIAM)">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7dys7zoberdktmxyjciuy5bnse" style="color: black;">SIAM journal on computing (Print)</a>
There are several results available in the literature dealing with efficient construction of t-spanners for a given set S of n points in R d . t-spanners are Euclidean graphs in which distances between vertices in G are at most t times the Euclidean distances between them; in other words, distances in G are "stretched" by a factor of at most t. We consider the interesting dual problem: given a Euclidean graph G whose vertex set corresponds to the set S, compute the stretch factor of G, i.e.,<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0097539799361671">doi:10.1137/s0097539799361671</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yfy67d5sqrakjnupd5kviksxdm">fatcat:yfy67d5sqrakjnupd5kviksxdm</a> </span>
more »... maximum ratio between distances in G and the corresponding Euclidean distances. It can trivially be solved by solving the All-Pairs-Shortest-Path problem. However, if an approximation to the stretch factor is sufficient, then we show it can be efficiently computed by making only O(n) approximate shortest path queries in the graph G. We apply this surprising result to obtain efficient algorithms for approximating the stretch factor of Euclidean graphs such as paths, cycles, trees, planar graphs, and general graphs. The main idea behind the algorithm is to use Callahan and Kosaraju's well-separated pair decomposition.
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829081537/https://users.cs.fiu.edu/~giri/papers/stretch.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/dc/f3/dcf391591a43674d82b4cba11356298b8d4528e0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0097539799361671"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>