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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Exact algorithm</span></span>
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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>In <a href="Computer_science" title="Computer science">computer science</a> and <a href="Operations_research" title="Operations research">operations research</a>, <b>exact algorithms</b> are <a href="Algorithm" title="Algorithm">algorithms</a> that always solve an optimization problem to optimality.
</p><p>Unless <a href="P_%3D_NP" class="mw-redirect" title="P = NP">P = NP</a>, an exact algorithm for an <a href="NP-hardness" title="NP-hardness"> NP-hard</a> optimization problem cannot run in worst-case <a href="Polynomial_time" class="mw-redirect" title="Polynomial time">polynomial time</a>. There has been extensive research on finding exact algorithms whose running time is exponential with a low base.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>
<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>
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<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Approximation-preserving_reduction" title="Approximation-preserving reduction">Approximation-preserving reduction</a></li>
<li><a href="APX" title="APX">APX</a> is the class of problems with some constant-factor approximation algorithm</li>
<li><a href="Heuristic_algorithm" class="mw-redirect" title="Heuristic algorithm">Heuristic algorithm</a></li>
<li><a href="Polynomial-time_approximation_scheme" title="Polynomial-time approximation scheme">PTAS</a> - a type of approximation algorithm that takes the approximation ratio as a parameter</li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><cite id="CITEREFFominKaski2013" class="citation cs2">Fomin, Fedor V.; Kaski, Petteri (March 2013), <a rel="nofollow" class="external text" href="http://cacm.acm.org/magazines/2013/3/161189-exact-exponential-algorithms/fulltext">"Exact Exponential Algorithms"</a>, <i><a href="Communications_of_the_ACM" title="Communications of the ACM">Communications of the ACM</a></i>, <b>56</b> (3): <span class="nowrap">80–</span>88, <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F2428556.2428575">10.1145/2428556.2428575</a></cite>.</span>
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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite id="CITEREFFominKratsch2010" class="citation book cs1">Fomin, Fedor V.; Kratsch, Dieter (2010). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/exactexponential00fvfo"><i>Exact Exponential Algorithms</i></a></span>. Springer. p. <a rel="nofollow" class="external text" href="https://archive.org/details/exactexponential00fvfo/page/n217">203</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-642-16532-0</bdi>.</cite></span>
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