A Modification of the Landau-Vishkin Algorithm Computing Longest Common Extensions via Suffix Arrays

Approximate string matching is an essential problem in many areas related to Computer Science including biological sequence processing. The standard solution of this problem is an O(mn) running time and space dynamic programming algorithm for two strings of length m and n. Landau and Vishkin developed an algorithm which uses suffix trees for accelerating the computation along the dynamic programming table and reaching space and running time in O(nk), where n > m and k is the maximum number of admissible differences. Suffix trees are used for preprocessing the sequences allowing an O(1) running time computation of the longest common extensions between substrings. One of the practical drawbacks of the Landau-Vishkin algorithm is the excessive use of space inherent to the use of suffix trees. In fact, although suffix trees can be handled in linear space their construction and manipulation implies high multiplying factors to this linear behavior. We present a variation of the Landau-Vishkin algorithm which instead of suffix trees uses suffix arrays for computing the longest common extensions, thereby improving actual space usage.