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    <p>Levenshtein distance will not completely work, because you want to allow rearrangements. I think your best bet is going to be to find best rearrangement with levenstein distance as cost for each word.</p> <p>To find the cost of rearrangement, kinda like the <a href="http://mathworld.wolfram.com/PancakeSorting.html" rel="noreferrer">pancake sorting problem</a>. So, you can permute every combination of words (filtering out exact matches), with every combination of other string, trying to minimize a combination of permute distance and Levenshtein distance on each word pair.</p> <p><em>edit:</em> Now that I have a second I can post a quick example (all 'best' guesses are on inspection and not actually running the algorithms):</p> <pre><code>original strings | best rearrangement w/ lev distance per word Into the clear blue sky | Into the c_lear blue sky The color is sky blue | is__ the colo_r blue sky R_dist = dist( 3 1 2 5 4 ) --&gt; 3 1 2 *4 5* --&gt; *2 1 3* 4 5 --&gt; *1 2* 3 4 5 = 3 L_dist = (2D+S) + (I+D+S) (Total Subsitutions: 2, deletions: 3, insertion: 1) </code></pre> <p>(notice all the flips include all elements in the range, and I use ranges where Xi - Xj = +/- 1) </p> <p>Other example</p> <pre><code>original strings | best rearrangement w/ lev distance per word Into the clear blue sky | Into the clear blue sky In the blue clear sky | In__ the clear blue sky R_dist = dist( 1 2 4 3 5 ) --&gt; 1 2 *3 4* 5 = 1 L_dist = (2D) (Total Subsitutions: 0, deletions: 2, insertion: 0) </code></pre> <p>And to show all possible combinations of the three...</p> <pre><code>The color is sky blue | The colo_r is sky blue In the blue clear sky | the c_lear in sky blue R_dist = dist( 2 4 1 3 5 ) --&gt; *2 3 1 4* 5 --&gt; *1 3 2* 4 5 --&gt; 1 *2 3* 4 5 = 3 L_dist = (D+I+S) + (S) (Total Subsitutions: 2, deletions: 1, insertion: 1) </code></pre> <p>Anyway you make the cost function the second choice will be lowest cost, which is what you expected!</p>
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    1. COHa -- I answered Levenstein distance on that one, too :P I'm not sure I'm smart enough to grok the paper you referenced in that one though 0.o
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