Computing a longest common subsequence that is almost increasing on sequences having no repeated elements

Given two permutations A and B   of [1..n][1..n] and a fixed constant c, we introduce the notion of a longest common almost increasing subsequence (LCAIS) as a longest common subsequence that can be converted to an increasing subsequence by possibly adding a value, that is at most c  , to each of the elements. We present an algorithm for computing LCAIS in O(n2)O(n2) space, O(n(n+c2))O(n(n+c2)) time.