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Phasing Data from Genotype Queries via the μ-PBWT

Authors: Davide Cozzi, Paola Bonizzoni, Christina Boucher, Ben Langmead, and Yuri Pirola

Published in: OASIcs, Volume 131, The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday (2025)

Abstract

Genotype phasing - the process of reconstructing haplotypes from genotype data - is a fundamental problem in genomics with applications in ancestry inference, imputation, and disease association. Traditional phasing methods rely on statistical models or combinatorial approaches which can be computationally expensive, particularly when applied to large-scale reference panels. In this paper, we present a first exploration of using the μ-PBWT (a run-length encoded Positional Burrows-Wheeler Transform) to solve the genotype phasing problem with a reference panel. Leveraging our previous results on positional substrings, we propose an approach that can explain a query genotype if the corresponding haplotype pair exists in the input panel. Moreover, our method is extended to cases where such a pair does not exist, even though some regions should remain unphased if they cannot be explicitly explained using the reference panel. We implemented this method and compared it against Beagle, a state-of-the-art phasing tool, demonstrating that, in the absence of mutations and recombinations, our approach correctly identifies the haplotype pair that explains a genotype query while using seven times less memory than Beagle. However, we also observe that as mutation rates increase, the quality of the phasing decreases as a result of the growing difficulty of identifying consistent haplotype pairs in the presence of sequence variation. These findings highlight the potential of μ-PBWT as an efficient alternative for genotype phasing, particularly in settings where computational resources are limited. The source code is publicly available at https://github.com/dlcgold/muPBWT/tree/phase.

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Davide Cozzi, Paola Bonizzoni, Christina Boucher, Ben Langmead, and Yuri Pirola. Phasing Data from Genotype Queries via the μ-PBWT. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cozzi_et_al:OASIcs.Manzini.10,
  author =	{Cozzi, Davide and Bonizzoni, Paola and Boucher, Christina and Langmead, Ben and Pirola, Yuri},
  title =	{{Phasing Data from Genotype Queries via the \mu-PBWT}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{10:1--10:17},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-390-4},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{131},
  editor =	{Ferragina, Paolo and Gagie, Travis and Navarro, Gonzalo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Manzini.10},
  URN =		{urn:nbn:de:0030-drops-239183},
  doi =		{10.4230/OASIcs.Manzini.10},
  annote =	{Keywords: Positional Burrows-Wheeler Transform, r-index, minimal position substring cover, set-maximal exact matches, genotype phasing}
}

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DOI: 10.4230/LIPIcs.CPM.2024.12

Solving the Minimal Positional Substring Cover Problem in Sublinear Space

Authors: Paola Bonizzoni, Christina Boucher, Davide Cozzi, Travis Gagie, and Yuri Pirola

Published in: LIPIcs, Volume 296, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)

Abstract

Within the field of haplotype analysis, the Positional Burrows-Wheeler Transform (PBWT) stands out as a key innovation, addressing numerous challenges in genomics. For example, Sanaullah et al. introduced a PBWT-based method that addresses the haplotype threading problem, which involves representing a query haplotype through a minimal set of substrings. To solve this problem using the PBWT data structure, they formulate the Minimal Positional Substring Cover (MPSC) problem, and then, subsequently present a solution for it. Additionally, they present and solve several variants of this problem: k-MPSC, leftmost MPSC, rightmost MPSC, and length-maximal MPSC. Yet, a full PBWT is required for each of their solutions, which yields a significant memory usage requirement. Here, we take advantage of the latest results on run-length encoding the PBWT, to solve the MPSC in a sublinear amount of space. Our methods involve demonstrating that k-Set Maximal Exact Matches (k-SMEMs) can be computed in a sublinear amount of space via efficient computation of k-Matching Statistics (k-MS). This leads to a solution that requires sublinear space for, not only the MPSC problem, but for all its variations proposed by Sanaullah et al. Most importantly, we present experimental results on haplotype panels from the 1000 Genomes Project data that show the utility of these theoretical results. We conclusively demonstrate that our approach markedly decreases the memory required to solve the MPSC problem, achieving a reduction of at least two orders of magnitude compared to the method proposed by Sanaullah et al. This efficiency allows us to solve the problem on large versions of the problem, where other methods are unable to scale to. In summary, the creation of {μ}-PBWT paves the way for new possibilities in conducting in-depth genetic research and analysis on a large scale. All source code is publicly available at https://github.com/dlcgold/muPBWT/tree/k-smem.

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Paola Bonizzoni, Christina Boucher, Davide Cozzi, Travis Gagie, and Yuri Pirola. Solving the Minimal Positional Substring Cover Problem in Sublinear Space. In 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 296, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bonizzoni_et_al:LIPIcs.CPM.2024.12,
  author =	{Bonizzoni, Paola and Boucher, Christina and Cozzi, Davide and Gagie, Travis and Pirola, Yuri},
  title =	{{Solving the Minimal Positional Substring Cover Problem in Sublinear Space}},
  booktitle =	{35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-326-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{296},
  editor =	{Inenaga, Shunsuke and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2024.12},
  URN =		{urn:nbn:de:0030-drops-201225},
  doi =		{10.4230/LIPIcs.CPM.2024.12},
  annote =	{Keywords: Positional Burrows-Wheeler Transform, r-index, minimal position substring cover, set-maximal exact matches}
}

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Phasing Data from Genotype Queries via the μ-PBWT

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Solving the Minimal Positional Substring Cover Problem in Sublinear Space

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