Comparison of Strings Belonging to the Same Family

Abstract The comparison of strings belonging to the same family can be made through the construction of a long(est) Common Subsequence (CS) that reflects structural similarities that exist between these strings. The longest CS problem is NP-complete. In this paper, we present an O( N 2 × L 2 log 2 ( L )) algorithm, where N is the number of the strings and L is the maximum length, that constructs a CS, to a family of strings, made up bu longer words appearing, approximately, in the same positions in all the strings. During each iteration, our algorithm looks for the longest common words that appear, approximately, in the same positions in all the strings, then, filters the common words found, to keep just those that assure the smallest norm between all the strings. The filtering is based on a new distance called contextual distance .

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