We define the unrestricted modified edit distance based on the modified edit distance defined by Galil and Giancarlo (1989) where the cost of substring deletions and insertions are contextsensitive and the cost of character substitutions are context-free. The modified edit distance is the minimum cost of converting a string X to a string Y where the sequence of edit operations has the property ...

In this paper, we provide a method for determining the asymptotic value of the maximum edit distance from a given hereditary property. This method permits the edit distance to be computed without using Szemerédi’s Regularity Lemma directly. Using this new method, we are able to compute the edit distance from hereditary properties for which it was previously unknown. For some graphs H, the edit ...

We survey the problem of comparing labeled trees based on simple local operations of deleting, inserting and relabeling nodes. These operations lead to the tree edit distance, alignment distance and inclusion problem. For each problem we review the results available and present, in detail, one or more of the central algorithms for solving the problem.

We build a functorial pipeline for persistent homology. The input to this is filtered simplicial complex indexed by any finite metric lattice, and the output persistence diagram defined as Möbius inversion of its birth-death function. adapt Reeb graph edit distance each our categories prove that both functors in are 1-Lipschitz, making stable. Our constructions generalize classical diagram, set...