Approximate String Searching under Weighted Edit Distance

Let p 2 be a string of length m and t 2 be a string of length n. The approximate string searching problem is to nd all approximate matches of p in t having weighted edit distance at most k from p. We present a new method that preprocesses the pattern into a DFA which scans t online in linear time, thereby recognizing all positions in t where an approximate match ends. We show how to reduce the exponential preprocessing eeort and propose two practical algorithms. The rst algorithm constructs the states of the DFA up to a certain depth r 1. It runs in O(jj r+1 m + q m + n) time and O(jj r+1 + jj r m) space where q n decreases as r increases. The second algorithm constructs the transitions of the DFA when they are demanded. It runs in O(qs jj+qt m+n) time and O(qs (jj+m)) space where qs qt n depend on the problem instance. Practical measurements show that our algorithms work well in practice and beat previous methods for problems of interest in molecular biology.