How Hard Is Computing the Edit Distance?

Efficiently Computing Edit Distance to Dyck Language

Given a string σ over alphabet Σ and a grammar G defined over the same alphabet, how many minimum number of repairs: insertions, deletions and substitutions are required to map σ into a valid member of G ? We investigate this basic question in this paper for DYCK(s). DYCK(s) is a fundamental context free grammar representing the language of well-balanced parentheses with s different types of pa...

The Reeb Graph Edit Distance is Universal

We consider the setting of Reeb graphs of piecewise linear functions and study distances between them that are stable, meaning that functions which are similar in the supremum norm ought to have similar Reeb graphs. We define an edit distance for Reeb graphs and prove that it is stable and universal, meaning that it provides an upper bound to any other stable distance. In contrast, via a specif...

Computing the Edit-Distance between Unrooted Ordered Trees

An ordered tree is a tree in which each node’s incident edges are cyclically ordered; think of the tree as being embedded in the plane. Let A and B be two ordered trees. The edit distance between A and B is the minimum cost of a sequence of operations (contract an edge, uncontract an edge, modify the label of an edge) needed to transform A into B. We give an O(n logn) algorithm to compute the e...

Bipartite Graph Matching for Computing the Edit Distance of Graphs

Computing the edit distance of a regular language

The edit distance (or Levenshtein distance) between two words is the smallest number of substitutions, insertions, and deletions of symbols that can be used to transform one of the words into the other. In this paper we consider the problem of computing the edit distance of a regular language (also known as constraint system), that is, the set of words accepted by a given finite automaton. This...