Summary: Faster Algorithms for String Matching with k Mismatches
Amihood Amir \Lambday Moshe Lewenstein \Lambda z Ely Porat \Lambda
Bar­Ilan University and Bar­Ilan University Bar Ilan University and
Georgia Tech Weizmann Institute
June 28, 2000
Abstract
The string matching with mismatches problem is that of finding the number of mismatches
between a pattern P of length m and every length m substring of the text T . Currently,
the fastest algorithms for this problem are the following. The Landau­Vishkin algorithm finds
all locations where the pattern has at most k errors (where k is part of the input) in time
O(nk). The Abrahamson algorithm finds the number of mismatches at every location in time
O(n
p
m log m).
We present an algorithm that is faster than both. Our algorithm finds all locations where
the pattern has at most k errors in time O(n
p
k log k). We also show an algorithm that solves
the above problem in time O((n + nk 3
m ) log k).

Source: Amir, Amihood - Computer Science Department, Bar Ilan University

Collections: Mathematics