Geometry and topology · Oct 6, 2026
The sharp exponential scale of edit-distance distortion
Determines the least distortion of embedding edit distance on words of length at most d into real ℓ1: it is . Insertions, deletions and substitutions have unit cost. The constants are uniform over all finite alphabets with at least two symbols, even when the alphabet grows with d; binary words already force the lower bound.
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