Given two strings X and Y over a finite alphabet, the edit distance between X and Y , d(X,Y ) is the number of elementary edit operations required to edit X into Y . A dynamic programming algorithm elegantly computes this distance. In this paper, we investigate the parallelization of calculating edit distance for a large set of strings using MapReduce, a popular parallel computing framework. We...

The edit distance between two graphs on the same labeled vertex set is the size of the symmetric difference of the edge sets. The distance between a graph, G, and a hereditary property, H, is the minimum of the distance between G and each G′ ∈ H with the same number of vertices. The edit distance function of H is a function of p ∈ [0, 1] and is the limit of the maximum normalized distance betwe...

String editing problem is one of the most fundamental problems in computer science and is used extensively in Bio-Informatics. In this thesis we present two new results relevant to the string editing problem. Firstly we show how we can simultaneously compute both the edit distance and edit script between two strings of length n in time O(n2/log(n)) and O(n) space. The Four Russian algorithm com...

with 3 edits (delete the C, delete the last A and insert a C). This is the best that can be done so the minimum edit distance is 3. The MED problem is an important problem that has many applications. For example in version control systems such as git or svn when you update a file and commit it, the system does not store the new version but instead only stores the “difference” from the previous ...

Several variants of the edit distance problem with block deletions are considered. Polynomial time optimal algorithms are presented for the edit distance with block deletions allowing character insertions and character moves, but without block moves. We show that the edit distance with block moves and block deletions is NP-complete (Nondeterministic Polynomial time problems in which any given s...