sequence (LCS) of those strings. If D is the simple Levenshtein distance between two strings having lengths m and n, SES is the length of the shortest edit sequence between the strings, and L is the length of an LCS of the strings, then SES = D and L = (m + n 0D)=2. We will focus on the problem of determining the length of an LCS and also on the related problem of recovering an LCS. Another related problem, which will be discussed in Chapter 7, is that of approximate string matching, in which it is desired to locate all positions within string y which begin an approximation to string x containing at most D errors (insertions or deletions). 124 SERIAL COMPUTATIONS OF LEVENSHTEIN DISTANCES procedure CLASSIC( x,<

this paper, in view of the particularly rich variety of algorithmic solutions that have been devised for this problem over the past two decades or so, which made it susceptible to some degrees of unification and systematization of independent and general interest. Our discussion starts with the exposition of two basic approaches to LCS computation, due respectively to Hirschberg [1978] and Hunt and Szymanski [1977]. We then discuss faster implementations of this second paradigm, and the data strucures that support them. In Section 5. we discuss algorithms that use only linear space to compute an LCS and yet do not necessarily take \Theta(nm) time. One, final, such algorithm is presented in section 6. where many of the ideas and tools accumulated in the course of our discussion find employment together. In Section 7. we make return to string editing in its general formulation and discuss some of its efficient solutions within a parallel model of computation.