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 x with another symbol. This problem has a well known O(lxl lyl) time sequential solution [25]. We give the efficient P R A M parallel algorithms for the string editing problem. If m=(Ixl, lyl) and n=max(lxl, lyl), then our CREW bound is @log rn log n) time with O(rnn/ log rn) processors. In all algorithms, space is O(rnn).Key words and phrases: Strint-to-string correction, edit distances, spelling correction, longest common subsequence, shortest paths, grid graphs, analysis of algorithms, parallel computation, cascading divide-and-conquer AMs subject classification: 68Q2.S 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).

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An O ( nL )-time algorithm is introduced for constructing an optimal Huffman code for a weighted alphabet of size n , where each code string must have length no greater than L . The algorithm uses O ( n ) space.

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