1 research outputs found
Longest common substring with approximately mismatches
In the longest common substring problem, we are given two strings of length
and must find a substring of maximal length that occurs in both strings. It
is well known that the problem can be solved in linear time, but the solution
is not robust and can vary greatly when the input strings are changed even by
one character. To circumvent this, Leimeister and Morgenstern introduced the
problem of the longest common substring with mismatches. Lately, this
problem has received a lot of attention in the literature. In this paper, we
first show a conditional lower bound based on the SETH hypothesis implying that
there is little hope to improve existing solutions. We then introduce a new but
closely related problem of the longest common substring with approximately
mismatches and use locality-sensitive hashing to show that it admits a solution
with strongly subquadratic running time. We also apply these results to obtain
a strongly subquadratic-time 2-approximation algorithm for the longest common
substring with mismatches problem and show conditional hardness of
improving its approximation ratio.Comment: extended version of a paper from CPM 2016 with corrected proof