7 Search Results for "Norri, Tuukka"

Document
Research
DOI: 10.4230/OASIcs.Grossi.2
On the Construction of Elastic Degenerate Strings

Authors: Nicola Rizzo, Veli Mäkinen, and Nadia Pisanti

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
An elastic degenerate string (EDS) is a sequence of sets of strings. In the context of bioinformatics, EDSes can be used to represent the variations observed in a population from its consensus genome. Pattern matching and comparison problems on EDSes have been widely studied in the literature, but their construction has been largely omitted. We fill this gap by showing how algorithms originally developed for related problems of founder reconstruction can be adapted to minimize the total cardinality of the EDS sets and total length of the EDS strings in linear time, given suitable multiple alignments representing the input data.
Cite as

Nicola Rizzo, Veli Mäkinen, and Nadia Pisanti. On the Construction of Elastic Degenerate Strings. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 2:1-2:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rizzo_et_al:OASIcs.Grossi.2,
  author =	{Rizzo, Nicola and M\"{a}kinen, Veli and Pisanti, Nadia},
  title =	{{On the Construction of Elastic Degenerate Strings}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{2:1--2:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.2},
  URN =		{urn:nbn:de:0030-drops-238014},
  doi =		{10.4230/OASIcs.Grossi.2},
  annote =	{Keywords: multiple sequence alignment, pattern matching, data structures, segmentation algorithms, founder reconstruction, dynamic programming, semi-dynamic range minimum queries, positional Burrows-Wheeler transform}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.7
Conditional Lower Bounds for String Matching in Labelled Graphs

Authors: Massimo Equi

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
The problem of String Matching in Labelled Graphs (SMLG) is one possible generalization of the classic problem of finding a string inside another of greater length. In its most general form, SMLG asks to find a match for a string into a graph, which can be directed or undirected. As for string matching, many different variations are possible. For example, the match could be exact or approximate, and the match could lie on a path or a walk. Some of these variations easily fall into the NP-hard realm, while other variants are solvable in polynomial time. For the latter ones, fine-grained complexity has been a game changer in proving quadratic conditional lower bounds, allowing to finally close the gap with those upper bounds that remained unmatched for almost two decades. If the match is allowed to be approximate, SMLG enjoys the same conditional quadratic lower bounds shown for example for edit distance (Backurs and Indyk, STOC '15). The case that really requires ad hoc conditional lower bounds is the one of finding an exact match that lies on a walk. In this work, we focus on explaining various conditional lower bounds for this version of SMLG, with the goal of giving an overall perspective that could help understand which aspects of the problem make it quadratic. We will introduce the reader to the field of fine-grained complexity and show how it can successfully provide the exact type of lower bounds needed for polynomial problems such as SMLG.
Cite as

Massimo Equi. Conditional Lower Bounds for String Matching in Labelled Graphs. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 7:1-7:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{equi:OASIcs.Grossi.7,
  author =	{Equi, Massimo},
  title =	{{Conditional Lower Bounds for String Matching in Labelled Graphs}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{7:1--7:13},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.7},
  URN =		{urn:nbn:de:0030-drops-238063},
  doi =		{10.4230/OASIcs.Grossi.7},
  annote =	{Keywords: conditional lower bounds, strong exponential time hypothesis, fine-grained complexity, string matching, graphs}
}
Document
DOI: 10.4230/OASIcs.Manzini.13
Graph Indexing Beyond Wheeler Graphs

Authors: Jarno N. Alanko, Elena Biagi, Massimo Equi, Veli Mäkinen, Simon J. Puglisi, Nicola Rizzo, Kunihiko Sadakane, and Jouni Sirén

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

Abstract
After the discovery of the FM index, which linked the Burrows-Wheeler transform (BWT) to pattern matching on strings, several contemporaneous strands of research began on indexing more complex structures with the BWT, such as tries, finite languages, de Bruijn graphs, and aligned sequences. These directions can now be viewed as culminating in the theory of Wheeler Graphs, but sometimes they go beyond. This chapter reviews the significant body of "proto Wheeler Graph" indexes, many of which exploit characteristics of their specific case to outperform Wheeler graphs, especially in practice.
Cite as

Jarno N. Alanko, Elena Biagi, Massimo Equi, Veli Mäkinen, Simon J. Puglisi, Nicola Rizzo, Kunihiko Sadakane, and Jouni Sirén. Graph Indexing Beyond Wheeler Graphs. In The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 131, pp. 13:1-13:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{alanko_et_al:OASIcs.Manzini.13,
  author =	{Alanko, Jarno N. and Biagi, Elena and Equi, Massimo and M\"{a}kinen, Veli and Puglisi, Simon J. and Rizzo, Nicola and Sadakane, Kunihiko and Sir\'{e}n, Jouni},
  title =	{{Graph Indexing Beyond Wheeler Graphs}},
  booktitle =	{The Expanding World of Compressed Data: A Festschrift for Giovanni Manzini's 60th Birthday},
  pages =	{13:1--13:29},
  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.13},
  URN =		{urn:nbn:de:0030-drops-239215},
  doi =		{10.4230/OASIcs.Manzini.13},
  annote =	{Keywords: indexing, compression, compressed data structures, string algorithms, pattern matching}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.29
Faster Approximate Elastic-Degenerate String Matching - Part B

Authors: Paweł Gawrychowski, Adam Górkiewicz, Pola Marciniak, Solon P. Pissis, and Karol Pokorski

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
We revisit the complexity of approximate pattern matching in an elastic-degenerate string. Such a string is a sequence of n finite sets of strings of total length N, and compactly describes a collection of strings obtained by first choosing exactly one string in every set, and then concatenating them together. This is motivated by the need of storing a collection of highly similar DNA sequences. The basic algorithmic question on elastic-degenerate strings is pattern matching: given such an elastic-degenerate string and a standard pattern of length m, check if the pattern occurs in one of the strings in the described collection. Bernardini et al. [SICOMP 2022] showed how to leverage fast matrix multiplication to obtain an Õ(nm^{ω-1})+𝒪(N)-time complexity for this problem, where ω is the matrix multiplication exponent. However, from the point of view of possible applications, it is more desirable to work with approximate pattern matching, where we seek approximate occurrences of the pattern. This generalization has been considered in a few papers already, but the best result so far for occurrences with k mismatches, where k is a constant, is the Õ(nm²+N)-time algorithm presented in Part A [CPM 2025]. This brings the question whether increasing the dependency on m from m^{ω-1} to quadratic is necessary when moving from k = 0 to larger (but still constant) k. We design an Õ(nm^{1.5}+N)-time algorithm for pattern matching with k mismatches in an elastic-degenerate string, for any constant k. To obtain this time bound, we leverage the structural characterization of occurrences with k mismatches of Charalampopoulos, Kociumaka, and Wellnitz [FOCS 2020] together with fast Fourier transform. We need to work with multiple patterns at the same time, instead of a single pattern, which requires refining the original characterization. This might be of independent interest.
Cite as

Paweł Gawrychowski, Adam Górkiewicz, Pola Marciniak, Solon P. Pissis, and Karol Pokorski. Faster Approximate Elastic-Degenerate String Matching - Part B. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 29:1-29:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gawrychowski_et_al:LIPIcs.CPM.2025.29,
  author =	{Gawrychowski, Pawe{\l} and G\'{o}rkiewicz, Adam and Marciniak, Pola and Pissis, Solon P. and Pokorski, Karol},
  title =	{{Faster Approximate Elastic-Degenerate String Matching - Part B}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{29:1--29:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.29},
  URN =		{urn:nbn:de:0030-drops-231236},
  doi =		{10.4230/LIPIcs.CPM.2025.29},
  annote =	{Keywords: ED string, approximate pattern matching, Hamming distance, k mismatches}
}
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.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.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.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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