String Editing and Longest Common

The string editing problem for input strings x and y consists of transforming x into y by performing a series of weighted edit operations on x of overall minimum cost. An edit operation on x can be the deletion of a symbol from x, the insertion of a symbol in x or the substitution of a symbol of x with another symbol. String editing models a variety of problems arising in such diverse areas as text and speech processing, geology and, last but not least, molecular biology. Special cases of string editing include the longest common subsequence problem, local alignment and similarity searching in DNA and protein sequences, and approximate string searching. We describe serial and parallel algorithmic solutions for the problem and some of its basic variants.