Linear time minimum segmentation enables scalable founder reconstruction

Abstract

Background We study a preprocessing routine relevant in pan-genomic analyses: consider a set of aligned haplotype sequences of complete human chromosomes. Due to the enormous size of such data, one would like to represent this input set with a few founder sequences that retain as well as possible the contiguities of the original sequences. Such a smaller set gives a scalable way to exploit pan-genomic information in further analyses (e.g. read alignment and variant calling). Optimizing the founder set is an NP-hard problem, but there is a segmentation formulation that can be solved in polynomial time, defined as follows. Given a threshold L and a set of m strings (haplotype sequences), each having length n , the minimum segmentation problem for founder reconstruction is to partition [1, n ] into set P of disjoint segments such that each segment has length at least L and the number of distinct substrings at segment [ a , b ] is minimized over . The distinct substrings in the segments represent founder blocks that can be concatenated to form founder sequences representing the original such that crossovers happen only at segment boundaries. Results We give an O ( mn ) time (i.e. linear time in the input size) algorithm to solve the minimum segmentation problem for founder reconstruction, improving over an earlier . Conclusions Our improvement enables to apply the formulation on an input of thousands of complete human chromosomes. We implemented the new algorithm and give experimental evidence on its practicality. The implementation is available in https://github.com/tsnorri/founder-sequences .

Reference flow: reducing reference bias using multiple population genomes

“…Such an optimization approach might improve coverage (and therefore accuracy) while removing the random element. This might be accomplished using unsupervised, sequence-driven clustering methods [34,35], using the "founder sequence" framework [36,37], or using some form of submodular optimization [38]. A more radical idea is to simply index all available individuals, forgoing the need to choose representatives; this is becoming more practical with the advent of new approaches for haplotype-aware path indexing [31] and efficient indexing for repetitive texts [39].…”

Pandora: nucleotide-resolution bacterial pan-genomics with reference graphs

“…Our approach, building from local MSAs and only collapsing haplotypes when they agree for a fixed number of bases, preserves more haplotype structure and avoids combinatorial explosion. Another alternative approach was recently taken by Norri et al [ 51 ], inferring a set of pseudo founder genomes from which to build the graph.…”

Reducing reference bias using multiple population reference genomes

“…Such an optimization approach might improve coverage (and therefore accuracy) while removing the random element. This might be accomplished using unsupervised, sequence-driven clustering methods 36,37 , using the "founder sequence" framework 38,39 , or using some form of submodular optimization 40 . A more radical idea is to simply index all available individuals, forgoing the need to choose representatives; this is becoming more practical with the advent of new approaches for haplotype-aware path indexing 33 and efficient indexing for repetitive texts 41 .…”