  The {\em longest common subsequence (LCS)} problem is a classic and
well-studied problem in computer science. Palindrome is a word which reads the
same forward as it does backward. The {\em longest common palindromic
subsequence (LCPS)} problem is an interesting variant of the classic LCS
problem which finds the longest common subsequence between two given strings
such that the computed subsequence is also a palindrome. In this paper, we
study the LCPS problem and give efficient algorithms to solve this problem. To
the best of our knowledge, this is the first attempt to study and solve this
interesting problem.
