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<head>
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<title>Droplet Sequenz Generator</title>
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<section>
<h4> Basic Idea </h4>
<img src="img/basic-idea.svg" align="center">
</section>
<section>
<h4> Multiple Paths </h4>
<img src="img/multiple-paths.svg" align="center">
</section>
<section>
<h4> Sequence Tuple</h4>
<ul>
<li> Generate multiple possible sequences </li>
<li> (Droplet, Path, Current Bifurcation, minSteps, maxSteps) </li>
</ul>
</section>
<section>
<h4> Algorithm to generate all possible sequences </h4>
<ul>
<li> Start with Payload Droplet at last Bifurcation in its path </li>
</ul>
<pre><code class="hljs" data-trim contenteditable>
if headerDroplet needed:
for all possible header droplet paths:
add header droplet to list of sequenceTuples
add list of sequenceTuples to list of possible Sequences
</pre></code>
</section>
<section>
<h4> Algorithm to generate all possible sequences </h4>
<ul>
<li> List of possible Sequences</li>
<li> { { (Pld, Path, currBif, 0,0),(Hdr-A, H-A-Path, curBif, minOffset-A, maxOffset-A)} <br>{ (Pld, Path, currBif, 0,0),(Hdr-B, H-B-Path, curBif, minOffset-B, maxOffset-B) } }</li>
</ul>
</section>
<section>
<h4> Algorithm to generate all possible sequences </h4>
<ul>
<li> Ascend the Path recursively for every Droplet and decide at every Bifurcation if another heder droplet is needed</li>
<li> This generates a (possibly huge) list of possibleSequences </li>
</ul>
</section>
<section>
<h4> Derive Droplet Sequence from list of possible sequences </h4>
<ul>
<li> Not every entry in the list of possible sequences represents a feasible sequence (e.g. same start time for 2 droplets) </li>
</ul>
<pre><code class="hljs" data-trim contenteditable>
sort list of possible sequences according to their length
take shortest sequence
if sequence is feasible and droplets don't coalesce:
return found sequence
else:
move on to next sequence
</pre></code>
</section>
<section>
<h4> Possible Improvements</h4>
<ul>
<li>Performance ! </li>
<li>Recursion for finding possible sequences not implemented with good performance</li>
<ol>
<li>Check paths for header droplets that are likely to produce a short (with a lower amount of header droplets) sequence </li>
<li>After all possible sequences for these few paths are found check for feasability and colesceing </li>
<li>Just in case no sequence was found check the more complicated possible sequences</li>
</ol>
<li>No verfication yet (that the sequence really realizes the correct payload path) </li>
</ul>
</section>
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