On finding a longest common palindromic subsequence

Recently, Chowdhury et al. [5] proposed the longest common palindromic subsequence problem. It is a variant of the well-known LCS problem, which refers to finding a palindromic LCS between two strings T1 and T2. In this paper, we present a new O(n+R2)-time algorithm where n=|T1|=|T2| and R is the number of matches between T1 and T2. We also show that the average running time of our algorithm is O(n4/|Σ|2), where Σ is the alphabet of T1 and T2. This improves the previously best algorithms whose running times are O(n4) and O(R2log2⁡nlog⁡log⁡n).