 
Summary: Modifications of the LandauVishkin Algorithm
Computing Longest Common Extensions via Suffix
Arrays and Efficient RMQ computations
Rodrigo C´esar de Castro Miranda1
, Mauricio AyalaRinc´on1
, and Leon Solon1
Instituto de Ci^encias Exatas,Universidade de Bras´ilia
rodrigo.miranda@acm.org,ayala@mat.unb.br,leonsolon@gmail.com
Abstract. Approximate string matching is an important problem in Computer
Science. The standard solution for this problem is an O(mn) running time and
space dynamic programming algorithm for two strings of length m and n. Lan
dau 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 ad
missible differences. In the Landau and Vishkin algorithm suffix trees are used
for preprocessing the sequences allowing an O(1) running time computation of
the longest common extensions between substrings. We present two O(n) space
variations of the Landau and Vishkin algorithm that use rangeminimumqueries
(RMQ) over the longest common prefix array of an extended suffix array instead
of suffix trees for computing the longest common extensions: one which computes
