3 Search Results for "Norri, Tuukka"

Document
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.
Cite as

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-dev.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}
}
Document
DOI: 10.4230/LIPIcs.WABI.2020.7
Linear Time Construction of Indexable Founder Block Graphs

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

Published in: LIPIcs, Volume 172, 20th International Workshop on Algorithms in Bioinformatics (WABI 2020)

Abstract
We introduce a compact pangenome representation based on an optimal segmentation concept that aims to reconstruct founder sequences from a multiple sequence alignment (MSA). Such founder sequences have the feature that each row of the MSA is a recombination of the founders. Several linear time dynamic programming algorithms have been previously devised to optimize segmentations that induce founder blocks that then can be concatenated into a set of founder sequences. All possible concatenation orders can be expressed as a founder block graph. We observe a key property of such graphs: if the node labels (founder segments) do not repeat in the paths of the graph, such graphs can be indexed for efficient string matching. We call such graphs segment repeat-free founder block graphs. We give a linear time algorithm to construct a segment repeat-free founder block graph given an MSA. The algorithm combines techniques from the founder segmentation algorithms (Cazaux et al. SPIRE 2019) and fully-functional bidirectional Burrows-Wheeler index (Belazzougui and Cunial, CPM 2019). We derive a succinct index structure to support queries of arbitrary length in the paths of the graph. Experiments on an MSA of SARS-CoV-2 strains are reported. An MSA of size 410× 29811 is compacted in one minute into a segment repeat-free founder block graph of 3900 nodes and 4440 edges. The maximum length and total length of node labels is 12 and 34968, respectively. The index on the graph takes only 3% of the size of the MSA.
Cite as

Veli Mäkinen, Bastien Cazaux, Massimo Equi, Tuukka Norri, and Alexandru I. Tomescu. Linear Time Construction of Indexable Founder Block Graphs. In 20th International Workshop on Algorithms in Bioinformatics (WABI 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 172, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{makinen_et_al:LIPIcs.WABI.2020.7,
  author =	{M\"{a}kinen, Veli and Cazaux, Bastien and Equi, Massimo and Norri, Tuukka and Tomescu, Alexandru I.},
  title =	{{Linear Time Construction of Indexable Founder Block Graphs}},
  booktitle =	{20th International Workshop on Algorithms in Bioinformatics (WABI 2020)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-161-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{172},
  editor =	{Kingsford, Carl and Pisanti, Nadia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2020.7},
  URN =		{urn:nbn:de:0030-drops-127961},
  doi =		{10.4230/LIPIcs.WABI.2020.7},
  annote =	{Keywords: Pangenome indexing, founder reconstruction, multiple sequence alignment, compressed data structures, string matching}
}
Document
DOI: 10.4230/LIPIcs.WABI.2018.15
Minimum Segmentation for Pan-genomic Founder Reconstruction in Linear Time

Authors: Tuukka Norri, Bastien Cazaux, Dmitry Kosolobov, and Veli Mäkinen

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)

Abstract
Given a threshold L and a set R = {R_1, ..., R_m} 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 [a,b] in P has length at least L and the number d(a,b)=|{R_i[a,b] : 1 <= i <= m}| of distinct substrings at segment [a,b] is minimized over [a,b] in P. The distinct substrings in the segments represent founder blocks that can be concatenated to form max{d(a,b) : [a,b] in P} founder sequences representing the original R such that crossovers happen only at segment boundaries. We give an optimal O(mn) time algorithm to solve the problem, improving over earlier O(mn^2). This improvement enables to exploit the algorithm on a pan-genomic setting of input strings being aligned haplotype sequences of complete human chromosomes, with a goal of finding a representative set of references that can be indexed for read alignment and variant calling. We implemented the new algorithm and give some experimental evidence on the practicality of the approach on this pan-genomic setting.
Cite as

Tuukka Norri, Bastien Cazaux, Dmitry Kosolobov, and Veli Mäkinen. Minimum Segmentation for Pan-genomic Founder Reconstruction in Linear Time. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{norri_et_al:LIPIcs.WABI.2018.15,
  author =	{Norri, Tuukka and Cazaux, Bastien and Kosolobov, Dmitry and M\"{a}kinen, Veli},
  title =	{{Minimum Segmentation for Pan-genomic Founder Reconstruction in Linear Time}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.15},
  URN =		{urn:nbn:de:0030-drops-93175},
  doi =		{10.4230/LIPIcs.WABI.2018.15},
  annote =	{Keywords: Pan-genome indexing, founder reconstruction, dynamic programming, positional Burrows-Wheeler transform, range minimum query}
}
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