Overlapping repetitions in weighted sequence

Abstract

Finding repeating patterns is a useful operation that have application in fields such as computing, music and molecular biology. In the latter, a requirement to detect repeating patterns in nucleic or protein sequences are very common in many applications such as the assembling of a genome from fragments. Finding covers and seeds of biological sequences have been equally important and useful operations in these fields. Algorithms that efficiently find covers and seeds of strings have been described in many papers. We focus in this paper on special cases of finding the shortest seeds in a weighted sequence with presence probability not less than a given threshold. Finding repeating patterns is a useful operation that have application in fields such as computing, music and molecular biology. In the latter, a requirement to detect repeating patterns in nucleic or protein sequences are very common in many applications such as the assembling of a genome from fragments. Finding covers and seeds of biological sequences have been equally important and useful operations in these fields. Algorithms that efficiently find covers and seeds of strings have been described in many papers. We focus in this paper on special cases of finding the shortest seeds in a weighted sequence with presence probability not less than a given threshold. A weighted sequence is a string in which a set of characters may appear at each position with respective probabilities of occurrence. In this paper we propose an O(nlogn) algorithm for finding the shortest seeds of a weighted sequence, where n is the cardinality of the input sequence, based on the algorithms for computing all the repeats of every length by using an iterative partitioning technique.