Finding a longest common subsequence between a run-length-encoded string and an uncompressed string

In this paper, we propose anO(min{mN,Mn}) time algorithm for finding a longest common subsequence of stringsX and Y with lengthsM andN , respectively, and run-length-encoded lengthsm and n, respectively. We propose a new recursive formula for finding a longest common subsequence of Y and X which is in the run-length-encoded format. That is, Y=y1y2 · · · yN andX=r1 1 r2 2 · · · rm m , where ri is the repeated character of run i and li is the number of its repetitions. There are three cases in the proposed recursive formula in which two cases are for ri matching yj . The third case is for ri mismatching yj . We will look specifically at the prior two cases that ri matches yj . To determine which case will be used when ri matches yj , we have to find a specific value which can be obtained by using another of our proposed recursive formulas. © 2007 Elsevier Inc. All rights reserved.