Efficient Parallel Algorithms for String Editing and Related Problems

The string editing problem for input strings z and y consists of transforming z into y by performing a series of weighted edit operations on z of overall minimum cost. An edit operation on z can be the deletion of a symbol from z, the insertion of a symbol in z or the substitution of a symbol of z with another symbol. This problem has a well known O( Izllvl) time sequential solution [25]. We give efficient PRAM parallel algorithms for the string editing problem. If m = min(lz1, Iyl) and n = max(1z1, Iyl), then our CREW bound is O(1og rn log n) time with O(rnn/ log rn) processors. Our CRCW bound is O((log n(1og log rn)2) time with O(mn/ log logrn) processors. In all algorithms, space is O(mn).