Finding All Tandem Arrays in DNA Sequences

A tandem array is a substring of the form k x , where x is any unspecific substring and k is at least two (when k is 2, 2 x is also called a tandem repeat or square). A non-extendable tandem array occurring in string S is a tandem array k x which are not followed or preceded by another occurrence of x in S. The problem of this thesis is defined as follows: Given a string S of length n, find all non-extendable tandem arrays of S. In the thesis, we present an O(nlogn) algorithm for the problem. The algorithm is based on a variation of an O(nlogn) algorithm for finding all squares in S. Instead of directly finding all non-extendable tandem arrays, we first find all squares and then use them to construct all non-extendable p-periodic substrings whose definition follows: A non-extendable p-periodic substring is a substring Y with maximal length m such that the ith character is equal to the ( ) p i + th character of Y for all { } p m 1 i − ∈ , ,K and ⎣ ⎦ 2 p m ≥ / . With all non-extendable p-periodic substrings found, we can easily determine all non-extendable tandem arrays at once.