string - Given the pairwise edit distance of a and b and b and c, can we find the pairwise edit distance of a and c? -

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if have 3 string a, b, c , know ( or calculated ) edit_distance(a,b) , edit_distance(b,c), can efficiently calculate edit_distance(a,c) without comparing , c.

*edit_distance(a,b) = number of character insertion, deletion , replacement required convert b.*

in general, no. example, take

  • a = cap
  • b = cat
  • c = car

here, edit_distance(a, b) = 1 , edit_distance(b, c) = 1. moreover, edit_distance(a, c) = 1.

however, have

  • a = cap
  • b = cat
  • c = rat

here, edit_distance(a, b) = 1 , edit_distance(b, c) = 1, edit_distance(a, c) = 2. therefore, there no way purely use edit distances of , b , of b , c compute edit distance of , c.

however, do know edit_distance(a, c) ≤ edit_distance(a, b) + edit_distance(b, c), since can apply transformations in sequence turn c. more generally, edit distance forms discrete distance metric, forms basis of bk-tree data structure.

hope helps!


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