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DOI: 10.4230/LIPIcs.ISAAC.2021.20

Algorithms and Complexity on Indexing Elastic Founder Graphs

Authors: Massimo Equi, Tuukka Norri, Jarno Alanko, Bastien Cazaux, Alexandru I. Tomescu, and Veli Mäkinen

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract

We study the problem of matching a string in a labeled graph. Previous research has shown that unless the Orthogonal Vectors Hypothesis (OVH) is false, one cannot solve this problem in strongly sub-quadratic time, nor index the graph in polynomial time to answer queries efficiently (Equi et al. ICALP 2019, SOFSEM 2021). These conditional lower-bounds cover even deterministic graphs with binary alphabet, but there naturally exist also graph classes that are easy to index: E.g. Wheeler graphs (Gagie et al. Theor. Comp. Sci. 2017) cover graphs admitting a Burrows-Wheeler transform -based indexing scheme. However, it is NP-complete to recognize if a graph is a Wheeler graph (Gibney, Thankachan, ESA 2019). We propose an approach to alleviate the construction bottleneck of Wheeler graphs. Rather than starting from an arbitrary graph, we study graphs induced from multiple sequence alignments. Elastic degenerate strings (Bernadini et al. SPIRE 2017, ICALP 2019) can be seen as such graphs, and we introduce here their generalization: elastic founder graphs. We first prove that even such induced graphs are hard to index under OVH. Then we introduce two subclasses that are easy to index. Moreover, we give a near-linear time algorithm to construct indexable elastic founder graphs. This algorithm is based on an earlier segmentation algorithm for gapless multiple sequence alignments inducing non-elastic founder graphs (Mäkinen et al., WABI 2020), but uses more involved techniques to cope with repetitive string collections synchronized with gaps. Finally, we show that one of the subclasses admits a reduction to Wheeler graphs in polynomial time.

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Massimo Equi, Tuukka Norri, Jarno Alanko, Bastien Cazaux, Alexandru I. Tomescu, and Veli Mäkinen. Algorithms and Complexity on Indexing Elastic Founder Graphs. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{equi_et_al:LIPIcs.ISAAC.2021.20,
  author =	{Equi, Massimo and Norri, Tuukka and Alanko, Jarno and Cazaux, Bastien and Tomescu, Alexandru I. and M\"{a}kinen, Veli},
  title =	{{Algorithms and Complexity on Indexing Elastic Founder Graphs}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.20},
  URN =		{urn:nbn:de:0030-drops-154532},
  doi =		{10.4230/LIPIcs.ISAAC.2021.20},
  annote =	{Keywords: orthogonal vectors hypothesis, multiple sequence alignment, segmentation}
}

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DOI: 10.4230/LIPIcs.WABI.2019.8

Finding All Maximal Perfect Haplotype Blocks in Linear Time

Authors: Jarno Alanko, Hideo Bannai, Bastien Cazaux, Pierre Peterlongo, and Jens Stoye

Published in: LIPIcs, Volume 143, 19th International Workshop on Algorithms in Bioinformatics (WABI 2019)

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. (Proceedings of BSB 2019) 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.

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Jarno Alanko, Hideo Bannai, Bastien Cazaux, Pierre Peterlongo, and Jens Stoye. Finding All Maximal Perfect Haplotype Blocks in Linear Time. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 8:1-8:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{alanko_et_al:LIPIcs.WABI.2019.8,
  author =	{Alanko, Jarno and Bannai, Hideo and Cazaux, Bastien and Peterlongo, Pierre and Stoye, Jens},
  title =	{{Finding All Maximal Perfect Haplotype Blocks in Linear Time}},
  booktitle =	{19th International Workshop on Algorithms in Bioinformatics (WABI 2019)},
  pages =	{8:1--8:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-123-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{143},
  editor =	{Huber, Katharina T. and Gusfield, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2019.8},
  URN =		{urn:nbn:de:0030-drops-110388},
  doi =		{10.4230/LIPIcs.WABI.2019.8},
  annote =	{Keywords: Population genomics, selection coefficient, haplotype block, positional Burrows-Wheeler Transform}
}

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Documents authored by Alanko, Jarno

Algorithms and Complexity on Indexing Elastic Founder Graphs

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Finding All Maximal Perfect Haplotype Blocks in Linear Time

Abstract

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