<p>Hi <a href="https://github.com/rcurtin" class="user-mention">@rcurtin</a> , I have run some tests with <em>mlpack_knn</em> and the <em>"Isolet"</em> dataset. It looks like it slightly faster when k is small, and the difference is greater for bigger values of k.<br>
Maybe, we should benchmark with bigger datasets like <em>"tinyImages100k"</em>. Also, it would be interesting to see the effect in other methods, like: <em>mlpack_cf</em>, <em>mlpack_lsh</em>, <em>mlpack_fastmks</em>, <em>mlpack_krann</em>, etc.</p>

<h1>Naive:</h1>

<ul>
<li>
<p><strong>No-heap:</strong></p>

<ul>
<li>k=3: total_time: 32.790772s</li>
<li>k=10: total_time: 32.946072s</li>
<li>k=20: total_time: 32.869260s</li>
<li>k=100: total_time: 33.801901s</li>
<li>k=1000: total_time: 52.723884s</li>
</ul>
</li>
<li>
<p><strong>Heap:</strong></p>

<ul>
<li>k=3: total_time: 31.996061s</li>
<li>k=10: total_time: 32.623913s</li>
<li>k=20: total_time: 32.756599s</li>
<li>k=100: total_time: 33.620033s</li>
<li>k=1000: total_time: 44.275435s </li>
</ul>
</li>
</ul>

<h1>Single-tree search:</h1>

<ul>
<li>
<p><strong>No-heap:</strong></p>

<ul>
<li>k=3: total_time: 19.419358s</li>
<li>k=10: total_time: 21.696434s</li>
<li>k=20: total_time: 23.501047s</li>
<li>k=100: total_time: 29.048157s</li>
<li>k=1000: total_time: 57.329319s</li>
</ul>
</li>
<li>
<p><strong>Heap:</strong></p>

<ul>
<li>k=3: total_time: 19.386155s</li>
<li>k=10: total_time: 21.643011s</li>
<li>k=20: total_time: 23.270618s</li>
<li>k=100: total_time: 29.031573s</li>
<li>k=1000: total_time: 50.519661s</li>
</ul>
</li>
</ul>

<h1>Dual-tree search:</h1>

<ul>
<li>
<p><strong>No-heap:</strong></p>

<ul>
<li>k=3: total_time: 15.207993s</li>
<li>k=10: total_time: 17.129599s</li>
<li>k=20: total_time: 18.325870s</li>
<li>k=100: total_time: 22.422410s</li>
<li>k=1000: total_time: 48.341919s</li>
</ul>
</li>
<li>
<p><strong>Heap:</strong></p>

<ul>
<li>k=3: total_time: 15.203970s</li>
<li>k=10: total_time: 16.998384s</li>
<li>k=20: total_time: 18.240207s</li>
<li>k=100: total_time: 22.401873s</li>
<li>k=1000: total_time: 41.206338s</li>
</ul>
</li>
</ul>

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