Abstract
Recent large-scale community sequencing efforts allow at an unprecedented level of detail the identification of genomic regions that show signatures of natural selection. Traditional methods for identifying such regions from individuals’ haplotype data, however, require excessive computing times and therefore are not applicable to current datasets. In 2019, Cunha et al. (Advances in bioinformatics and computational biology: 11th Brazilian symposium on bioinformatics, BSB 2018, Niterói, Brazil, October 30 - November 1, 2018, Proceedings, 2018. https://doi.org/10.1007/978-3-030-01722-4_3) suggested the maximal perfect haplotype block as a very simple combinatorial pattern, forming the basis of a new method to perform rapid genome-wide selection scans. The algorithm they presented for identifying these blocks, however, had a worst-case running time quadratic in the genome length. It was posed as an open problem whether an optimal, linear-time algorithm exists. In this paper we give two algorithms that achieve this time bound, one conceptually very simple one using suffix trees and a second one using the positional Burrows–Wheeler Transform, that is very efficient also in practice.
Highlights
Introduction and backgroundAs a result of the technological advances that went hand in hand with the genomics efforts of the last decades, today it is possible to experimentally obtain and study the genomes of large numbers of individuals, or even multiple samples from an individual
Considerably faster than previous methods, the running time of the algorithm presented in that paper is not optimal, as it takes O(kn2 ) time in order to find all maximal perfect haplotype blocks in k genomes of length n each
Our implementation has a user-defined parameter allowing to adjust the minimum size of a reported maximal perfect haplotype block (K, i, j), where size is defined as the width ( j − i + 1) times the number of rows (|K|) in the block
Summary
As a result of the technological advances that went hand in hand with the genomics efforts of the last decades, today it is possible to experimentally obtain and study the genomes of large numbers of individuals, or even multiple samples from an individual. Considerably faster than previous methods, the running time of the algorithm presented in that paper is not optimal, as it takes O(kn2 ) time in order to find all maximal perfect haplotype blocks in k genomes of length n each This is sufficient to analyse individual human chromosomes on a laptop computer, for datasets of the size of the 1000. Lemma 1 Suppose we have a maximal perfect haplotype block (K, i, j), the set {a−1 j [r] | r ∈ K } must be a contiguous range [x, y] of indices such that (i, j; x, y) is an available block Proof This necessary condition follows immediately from Definitions 1 and 2 and the definition of the pBWT (arrays al and dl ). VCF files and converting them to a binary haplotype ftp://ftp.1000genomes.ebi.ac.uk/vol1/ftp/release/20130502/
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