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Documents authored by Bonizzoni, Paola

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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.
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}
}
Document
DOI: 10.4230/LIPIcs.CPM.2020.6
On Two Measures of Distance Between Fully-Labelled Trees

Authors: Giulia Bernardini, Paola Bonizzoni, and Paweł Gawrychowski

Published in: LIPIcs, Volume 161, 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)

Abstract
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for comparing rooted trees representing the evolution of mutations in tumor phylogenies. Bernardini et al. [CPM 2019] recently introduced a notion of the rearrangement distance for fully-labelled trees motivated by this necessity. This notion originates from two operations: one that permutes the labels of the nodes, the other that affects the topology of the tree. Each operation alone defines a distance that can be computed in polynomial time, while the actual rearrangement distance, that combines the two, was proven to be NP-hard. We answer two open question left unanswered by the previous work. First, what is the complexity of computing the permutation distance? Second, is there a constant-factor approximation algorithm for estimating the rearrangement distance between two arbitrary trees? We answer the first one by showing, via a two-way reduction, that calculating the permutation distance between two trees on n nodes is equivalent, up to polylogarithmic factors, to finding the largest cardinality matching in a sparse bipartite graph. In particular, by plugging in the algorithm of Liu and Sidford [ArXiv 2020], we obtain an 𝒪̃(n^{4/3+o(1}) time algorithm for computing the permutation distance between two trees on n nodes. Then we answer the second question positively, and design a linear-time constant-factor approximation algorithm that does not need any assumption on the trees.
Cite as

Giulia Bernardini, Paola Bonizzoni, and Paweł Gawrychowski. On Two Measures of Distance Between Fully-Labelled Trees. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bernardini_et_al:LIPIcs.CPM.2020.6,
  author =	{Bernardini, Giulia and Bonizzoni, Paola and Gawrychowski, Pawe{\l}},
  title =	{{On Two Measures of Distance Between Fully-Labelled Trees}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{6:1--6:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{G{\o}rtz, Inge Li and Weimann, Oren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2020.6},
  URN =		{urn:nbn:de:0030-drops-121318},
  doi =		{10.4230/LIPIcs.CPM.2020.6},
  annote =	{Keywords: Tree distance, Cancer progression, Approximation algorithms, Fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.CPM.2019.28
A Rearrangement Distance for Fully-Labelled Trees

Authors: Giulia Bernardini, Paola Bonizzoni, Gianluca Della Vedova, and Murray Patterson

Published in: LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)

Abstract
The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the widely studied setting of classical phylogenetics, where trees are leaf-labelled, tumoral trees are fully labelled, i.e., every vertex has a label. In this paper we provide a rearrangement distance measure between two fully-labelled trees. This notion originates from two operations: one which modifies the topology of the tree, the other which permutes the labels of the vertices, hence leaving the topology unaffected. While we show that the distance between two trees in terms of each such operation alone can be decided in polynomial time, the more general notion of distance when both operations are allowed is NP-hard to decide. Despite this result, we show that it is fixed-parameter tractable, and we give a 4-approximation algorithm when one of the trees is binary.
Cite as

Giulia Bernardini, Paola Bonizzoni, Gianluca Della Vedova, and Murray Patterson. A Rearrangement Distance for Fully-Labelled Trees. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bernardini_et_al:LIPIcs.CPM.2019.28,
  author =	{Bernardini, Giulia and Bonizzoni, Paola and Della Vedova, Gianluca and Patterson, Murray},
  title =	{{A Rearrangement Distance for Fully-Labelled Trees}},
  booktitle =	{30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-103-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{128},
  editor =	{Pisanti, Nadia and P. Pissis, Solon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.28},
  URN =		{urn:nbn:de:0030-drops-104998},
  doi =		{10.4230/LIPIcs.CPM.2019.28},
  annote =	{Keywords: Tree rearrangement distance, Cancer progression, Approximation algorithms, Computational complexity}
}
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