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  1. PO
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    <p>This isn't an answer, but I think maybe a more precise or even more correct formulation of what you are looking for:</p> <p>There is a set, call it <code>C</code>, of <em>characters</em>, and there is a finite ordered sequence <code>S_1, ... S_n</code> of <em>scenes</em>, where a <em>scene</em> is a set consisting of some of the characters. Characters may (and typically do) appear in multiple scenes.</p> <p>I'd like to phrase your desired outcome in a slightly different way from how you phrased it, because I think it makes it clearer how one may search for a solution (or at least, it makes it totally clear how to brute-force a solution):</p> <p>The output of our algorithm is a sequence of arrangements of the characters. An <em>arrangement</em> of the characters is just a permutation of the ordered tuple <code>[c_1, ... c_m]</code>, where the <code>c_i</code> are the characters, and there are <code>m</code> of them in total, so <code>C = {c_1, ..., c_m}</code>. We want <code>n</code> arrangements in total, call them <code>A_1, ..., A_n</code>, one per scene.</p> <p>What arrangement <code>A_n</code> corresponds to is the top-to-bottom ordering of the characters in your storyboard, during scene <code>n</code>, in the following sense: draw a vertical line through your storyboard passing through scene <code>n</code>. This line should hit the characters' life-lines in the order specified by <code>A_n</code>.</p> <p>We require the following property of our arrangements: given scene <code>S_n</code>, the arrangement <code>A_n</code> needs to put the characters contained in <code>S_n</code> into a contiguous chunk, in the following sense: suppose that <code>S_n = {c_2, c_3, c_5}</code>. Then <code>A_n</code> may yield <code>[c_1, c_4, c_2, c_3, c_5]</code>, but may not yield <code>[c_2, c_1, c_3, c_4, c_5]</code>. This is because you don't want an errant character "cutting through" the scene in the storyboard.</p> <p>We hope to minimize the number of "crossings." Here, crossings are easy to define: the number of crossings between <code>A_i</code> and <code>A_(i+1)</code> is exactly equal to the number of <em>transpositions of adjacent characters</em> required to go from permutation <code>A_i</code> to permutation <code>A_(i+1)</code>.</p> <hr> <p>I haven't given you an answer, but I think that given the above setup, a brute-force approach isn't too hard to code up, and will give you an answer overnight without a problem, if the storyboard isn't too big.</p> <p>I think that if you posted this problem on MathOverflow, you could possibly get someone interested in it. Or maybe it has been solved, who knows?</p>
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    1. POIn search of an algorithm for sorting collection in nodes to satisfy a layout constraint
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    1. USAndrey Mishchenko
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    1. POIn search of an algorithm for sorting collection in nodes to satisfy a layout constraint
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    1. CONice formalism. Looks right to me. This was going to be for hundreds (maybe thousands at worst) of elements, and I was going to hopefully only generate them once every hour or so at worst. Guess I'll sleep on it some more.
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