Length of Maximal Common Subsequences

The problem of computing the length of the maximal common subsequences of two strings is quite well examined in the sequential case. There are many variations, but the standard approach is to compute the length in quadratic time using dynamic programming. A lineartime parallel algorithm can be obtained via a simple modification of this strategy by letting a linear number of processors sweep through the table created for the dynamic programming approach. However, the contribution of this paper is to show that the problem is in NC. More specifically, we show that the length of the maximal common subsequences of two strings s and t can be computed in time O(log|s|· log|t|) in the CREW PRAM model and in time Θ(min(log|s|, log|t|)) in the COMMON CRCW PRAM model.