A Linear-Space Algorithm for the Substring Constrained Alignment Problem
In a string similarity metric adopting affine gap penalties, we propose a quadratic-time, linear-space algorithm for the following constrained string alignment problem. The input of the problem is a pair of strings to be aligned and a pattern given as a string. Let an occurrence of the pattern in a string be a minimal substring of the string that is most similar to the pattern. Then, the output of the problem is a highest-scoring alignment of the pair of strings that matches an occurrence of the pattern in one string and an occurrence of the pattern in the other, where the score of the alignment excludes the similarity between the matched occurrences of the pattern. This problem may arise when we know that each of the strings has exactly one meaningful occurrence of the pattern and want to determine a putative pair of such occurrences based on homology of the strings.