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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}
}

Document

DOI: 10.4230/LIPIcs.SEA.2025.13

Pangenome Graph Indexing via the Multidollar-BWT

Authors: Davide Cozzi, Brian Riccardi, Luca Denti, Simone Ciccolella, Kunihiko Sadakane, and Paola Bonizzoni

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract

Indexing pangenome graphs is a major algorithmic challenge in computational pangenomics, a recent and active research field that seeks to use graphs as representations of multiple genomes. Since these graphs are constructed from whole genome sequences of a species population, they can become very large, making indexing one of the most challenging problems. In this paper, we propose gindex, a novel indexing approach to solve the Graph Pattern Matching Problem based on the multidollar-BWT. Specifically, gindex aims to find all occurrences of a pattern in a sequence-labeled graph by overcoming two main limitations of GCSA2, one of the most widely used graph indexes: handling queries of arbitrary length and scaling to large graphs without pruning any complex regions. Moreover, we show how a smart preprocessing step can optimize the use of multidollar-BWT to skip small redundant sub-patterns and enhance gindex’s querying capabilities. We demonstrate the effectiveness of our approach by comparing it to GCSA2 in terms of index construction and query time, using different preprocessing modes on three pangenome graphs: one built from Drosophila genomes and two produced by the Human Pangenome Reference Consortium. The results show that gindex can scale on human pangenome graphs - which GCSA2 cannot index using large amounts of RAM - with acceptable memory and time requirements. Moreover, gindex achieves fast query times, although not as fast as GCSA2, which may produce false positives.

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Davide Cozzi, Brian Riccardi, Luca Denti, Simone Ciccolella, Kunihiko Sadakane, and Paola Bonizzoni. Pangenome Graph Indexing via the Multidollar-BWT. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cozzi_et_al:LIPIcs.SEA.2025.13,
  author =	{Cozzi, Davide and Riccardi, Brian and Denti, Luca and Ciccolella, Simone and Sadakane, Kunihiko and Bonizzoni, Paola},
  title =	{{Pangenome Graph Indexing via the Multidollar-BWT}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.13},
  URN =		{urn:nbn:de:0030-drops-232515},
  doi =		{10.4230/LIPIcs.SEA.2025.13},
  annote =	{Keywords: Multidollar-BWT, Graph Index, Graph Pattern Matching, Pangenome Graph}
}

Artifact

Software

DOI: 10.4230/artifacts.22480

muPBWT k-SMEM

Authors: Davide Cozzi

Abstract

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Davide Cozzi. muPBWT k-SMEM (Software, Source code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@misc{dagstuhl-artifact-22480,
   title = {{muPBWT k-SMEM}}, 
   author = {Cozzi, Davide},
   note = {Software, European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement PANGAIA No. 87253, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:d3467768a54423c8294abfc44f87f18705b3ed02;origin=https://github.com/dlcgold/muPBWT;visit=swh:1:snp:e69e661f21c323ba367bb685b5cd0da27a8b0462;anchor=swh:1:rev:9dc88c898146ae314ceb58aef9daab6ba27caa8c}{\texttt{swh:1:dir:d3467768a54423c8294abfc44f87f18705b3ed02}} (visited on 2024-11-28)},
   url = {https://github.com/dlcgold/muPBWT/tree/k-smem},
   doi = {10.4230/artifacts.22480},
}

Document

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.

Cite as

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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Documents authored by Cozzi, Davide

Phasing Data from Genotype Queries via the μ-PBWT

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Pangenome Graph Indexing via the Multidollar-BWT

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muPBWT k-SMEM

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Solving the Minimal Positional Substring Cover Problem in Sublinear Space

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