6 Search Results for "Medvedev, Paul"


Document
Exact Sketch-Based Read Mapping

Authors: Tizian Schulz and Paul Medvedev

Published in: LIPIcs, Volume 273, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)


Abstract
Given a sequencing read, the broad goal of read mapping is to find the location(s) in the reference genome that have a "similar sequence". Traditionally, "similar sequence" was defined as having a high alignment score and read mappers were viewed as heuristic solutions to this well-defined problem. For sketch-based mappers, however, there has not been a problem formulation to capture what problem an exact sketch-based mapping algorithm should solve. Moreover, there is no sketch-based method that can find all possible mapping positions for a read above a certain score threshold. In this paper, we formulate the problem of read mapping at the level of sequence sketches. We give an exact dynamic programming algorithm that finds all hits above a given similarity threshold. It runs in {O}(|t| + |p| + 𝓁²) time and Θ(𝓁²) space, where |t| is the number of k-mers inside the sketch of the reference, |p| is the number of k-mers inside the read’s sketch and 𝓁 is the number of times that k-mers from the pattern sketch occur in the sketch of the text. We evaluate our algorithm’s performance in mapping long reads to the T2T assembly of human chromosome Y, where ampliconic regions make it desirable to find all good mapping positions. For an equivalent level of precision as minimap2, the recall of our algorithm is 0.88, compared to only 0.76 of minimap2.

Cite as

Tizian Schulz and Paul Medvedev. Exact Sketch-Based Read Mapping. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Copy BibTex To Clipboard

@InProceedings{schulz_et_al:LIPIcs.WABI.2023.14,
  author =	{Schulz, Tizian and Medvedev, Paul},
  title =	{{Exact Sketch-Based Read Mapping}},
  booktitle =	{23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-294-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{273},
  editor =	{Belazzougui, Djamal and Ouangraoua, A\"{i}da},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2023.14},
  URN =		{urn:nbn:de:0030-drops-186403},
  doi =		{10.4230/LIPIcs.WABI.2023.14},
  annote =	{Keywords: Sequence Sketching, Long-read Mapping, Exact Algorithm, Dynamic Programming}
}
Document
Compression Algorithm for Colored de Bruijn Graphs

Authors: Amatur Rahman, Yoann Dufresne, and Paul Medvedev

Published in: LIPIcs, Volume 273, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)


Abstract
A colored de Bruijn graph (also called a set of k-mer sets), is a set of k-mers with every k-mer assigned a set of colors. Colored de Bruijn graphs are used in a variety of applications, including variant calling, genome assembly, and database search. However, their size has posed a scalability challenge to algorithm developers and users. There have been numerous indexing data structures proposed that allow to store the graph compactly while supporting fast query operations. However, disk compression algorithms, which do not need to support queries on the compressed data and can thus be more space-efficient, have received little attention. The dearth of specialized compression tools has been a detriment to tool developers, tool users, and reproducibility efforts. In this paper, we develop a new tool that compresses colored de Bruijn graphs to disk, building on previous ideas for compression of k-mer sets and indexing colored de Bruijn graphs. We test our tool, called ESS-color, on various datasets, including both sequencing data and whole genomes. ESS-color achieves better compression than all evaluated tools and all datasets, with no other tool able to consistently achieve less than 44% space overhead.

Cite as

Amatur Rahman, Yoann Dufresne, and Paul Medvedev. Compression Algorithm for Colored de Bruijn Graphs. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 17:1-17:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Copy BibTex To Clipboard

@InProceedings{rahman_et_al:LIPIcs.WABI.2023.17,
  author =	{Rahman, Amatur and Dufresne, Yoann and Medvedev, Paul},
  title =	{{Compression Algorithm for Colored de Bruijn Graphs}},
  booktitle =	{23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-294-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{273},
  editor =	{Belazzougui, Djamal and Ouangraoua, A\"{i}da},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2023.17},
  URN =		{urn:nbn:de:0030-drops-186434},
  doi =		{10.4230/LIPIcs.WABI.2023.17},
  annote =	{Keywords: colored de Bruijn graphs, disk compression, k-mer sets, simplitigs, spectrum-preserving string sets}
}
Document
Invited Talk
Efficient Solutions to Biological Problems Using de Bruijn Graphs (Invited Talk)

Authors: Leena Salmela

Published in: LIPIcs, Volume 242, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)


Abstract
The de Bruijn graph has become a standard method in the analysis of sequencing reads in computational biology due to its ability to represent the information contained in large read sets in small space. A de Bruijn graph represents a set of sequencing reads by its k-mers, i.e. the set of substrings of length k that occur in the reads. In the classical definition, the k-mers are the edges of the graph and the nodes are the k-1 bases long prefixes and suffixes of the k-mers. Usually only k-mers occurring several times in the read set are kept to filter out noise in the data. De Bruijn graphs have been used to solve many problems in computational biology including genome assembly [Ramana M. Idury and Michael S. Waterman, 1995; Pavel A. Pevzner et al., 2001; Anton Bankevich et al., 2012; Yu Peng et al., 2010], sequencing error correction [Leena Salmela and Eric Rivals, 2014; Giles Miclotte et al., 2016; Leena Salmela et al., 2017; Limasset et al., 2019], reference free variant calling [Raluca Uricaru et al., 2015], indexing read sets [Camille Marchet et al., 2021], and so on. Next I will discuss two of these problems in more depth. The de Bruijn graph first emerged in computation biology in the context of genome assembly [Ramana M. Idury and Michael S. Waterman, 1995; Pavel A. Pevzner et al., 2001] where the task is to reconstruct a genome based on sequencing reads. As the de Bruijn graph can represent large read sets compactly, it became the standard approach to assemble short reads [Anton Bankevich et al., 2012; Yu Peng et al., 2010]. In the theoretical framework of de Bruijn graph based genome assembly, a genome is thought to be the Eulerian path in the de Bruijn graph built on the sequencing reads. In practise, the Eulerian path is not unique and thus not useful in the biological context. Therefore, practical implementations report subpaths that are guaranteed to be part of any Eulerian path and thus part of the actual genome. Such models include unitigs, which are nonbranching paths of the de Bruijn graph, and more involved definitions such as omnitigs [Alexandru I. Tomescu and Paul Medvedev, 2017]. In genome assembly the choice of k is a crucial matter. A small k can result in a tangled graph, whereas a too large k will fragment the graph. Furthermore, a different value of k may be optimal for different parts of the genome. Variable order de Bruijn graphs [Christina Boucher et al., 2015; Djamal Belazzougui et al., 2016], which represent de Bruijn graphs of all orders k in a single data structure, have been proposed as a solution but no rigorous definition corresponding to unitigs has been presented. We give the first definition of assembled sequences, i.e. contigs, on such graphs and an algorithm for enumerating them. Another problem that can be solved with de Bruijn graphs is the correction of sequencing errors [Leena Salmela and Eric Rivals, 2014; Giles Miclotte et al., 2016; Leena Salmela et al., 2017; Limasset et al., 2019]. Because each position of a genome is sequenced several times, it is possible to correct sequencing errors in reads if we can identify data originating from the same genomic region. A de Bruijn graph can be used to represent compactly the reliable information and the individual reads can be corrected by aligning them to the graph.

Cite as

Leena Salmela. Efficient Solutions to Biological Problems Using de Bruijn Graphs (Invited Talk). In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{salmela:LIPIcs.WABI.2022.1,
  author =	{Salmela, Leena},
  title =	{{Efficient Solutions to Biological Problems Using de Bruijn Graphs}},
  booktitle =	{22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)},
  pages =	{1:1--1:2},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-243-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{242},
  editor =	{Boucher, Christina and Rahmann, Sven},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2022.1},
  URN =		{urn:nbn:de:0030-drops-170357},
  doi =		{10.4230/LIPIcs.WABI.2022.1},
  annote =	{Keywords: de Bruijn graph, variable order de Bruijn graph, genome assembly, sequencing error correction, k-mers}
}
Document
A Graph-Theoretic Barcode Ordering Model for Linked-Reads

Authors: Yoann Dufresne, Chen Sun, Pierre Marijon, Dominique Lavenier, Cedric Chauve, and Rayan Chikhi

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


Abstract
Considering a set of intervals on the real line, an interval graph records these intervals as nodes and their intersections as edges. Identifying (i.e. merging) pairs of nodes in an interval graph results in a multiple-interval graph. Given only the nodes and the edges of the multiple-interval graph without knowing the underlying intervals, we are interested in the following questions. Can one determine how many intervals correspond to each node? Can one compute a walk over the multiple-interval graph nodes that reflects the ordering of the original intervals? These questions are closely related to linked-read DNA sequencing, where barcodes are assigned to long molecules whose intersection graph forms an interval graph. Each barcode may correspond to multiple molecules, which complicates downstream analysis, and corresponds to the identification of nodes of the corresponding interval graph. Resolving the above graph-theoretic problems would facilitate analyses of linked-reads sequencing data, through enabling the conceptual separation of barcodes into molecules and providing, through the molecules order, a skeleton for accurately assembling the genome. Here, we propose a framework that takes as input an arbitrary intersection graph (such as an overlap graph of barcodes) and constructs a heuristic approximation of the ordering of the original intervals.

Cite as

Yoann Dufresne, Chen Sun, Pierre Marijon, Dominique Lavenier, Cedric Chauve, and Rayan Chikhi. A Graph-Theoretic Barcode Ordering Model for Linked-Reads. In 20th International Workshop on Algorithms in Bioinformatics (WABI 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 172, pp. 11:1-11:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{dufresne_et_al:LIPIcs.WABI.2020.11,
  author =	{Dufresne, Yoann and Sun, Chen and Marijon, Pierre and Lavenier, Dominique and Chauve, Cedric and Chikhi, Rayan},
  title =	{{A Graph-Theoretic Barcode Ordering Model for Linked-Reads}},
  booktitle =	{20th International Workshop on Algorithms in Bioinformatics (WABI 2020)},
  pages =	{11:1--11:17},
  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.2020.11},
  URN =		{urn:nbn:de:0030-drops-128001},
  doi =		{10.4230/LIPIcs.WABI.2020.11},
  annote =	{Keywords: DNA sequencing, graph algorithms, linked-reads, interval graphs, cliques}
}
Document
Disk Compression of k-mer Sets

Authors: Amatur Rahman, Rayan Chikhi, and Paul Medvedev

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


Abstract
K-mer based methods have become prevalent in many areas of bioinformatics. In applications such as database search, they often work with large multi-terabyte-sized datasets. Storing such large datasets is a detriment to tool developers, tool users, and reproducibility efforts. General purpose compressors like gzip, or those designed for read data, are sub-optimal because they do not take into account the specific redundancy pattern in k-mer sets. In our earlier work (Rahman and Medvedev, RECOMB 2020), we presented an algorithm UST-Compress that uses a spectrum-preserving string set representation to compress a set of k-mers to disk. In this paper, we present two improved methods for disk compression of k-mer sets, called ESS-Compress and ESS-Tip-Compress. They use a more relaxed notion of string set representation to further remove redundancy from the representation of UST-Compress. We explore their behavior both theoretically and on real data. We show that they improve the compression sizes achieved by UST-Compress by up to 27 percent, across a breadth of datasets. We also derive lower bounds on how well this type of compression strategy can hope to do.

Cite as

Amatur Rahman, Rayan Chikhi, and Paul Medvedev. Disk Compression of k-mer Sets. In 20th International Workshop on Algorithms in Bioinformatics (WABI 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 172, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{rahman_et_al:LIPIcs.WABI.2020.16,
  author =	{Rahman, Amatur and Chikhi, Rayan and Medvedev, Paul},
  title =	{{Disk Compression of k-mer Sets}},
  booktitle =	{20th International Workshop on Algorithms in Bioinformatics (WABI 2020)},
  pages =	{16:1--16:18},
  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.2020.16},
  URN =		{urn:nbn:de:0030-drops-128057},
  doi =		{10.4230/LIPIcs.WABI.2020.16},
  annote =	{Keywords: de Bruijn graphs, compression, k-mer sets, spectrum-preserving string sets}
}
Document
Optimal Omnitig Listing for Safe and Complete Contig Assembly

Authors: Massimo Cairo, Paul Medvedev, Nidia Obscura Acosta, Romeo Rizzi, and Alexandru I. Tomescu

Published in: LIPIcs, Volume 78, 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)


Abstract
Genome assembly is the problem of reconstructing a genome sequence from a set of reads from a sequencing experiment. Typical formulations of the assembly problem admit in practice many genomic reconstructions, and actual genome assemblers usually output contigs, namely substrings that are promised to occur in the genome. To bridge the theory and practice, Tomescu and Medvedev [RECOMB 2016] reformulated contig assembly as finding all substrings common to all genomic reconstructions. They also gave a characterization of those walks (omnitigs) that are common to all closed edge-covering walks of a (directed) graph, a typical notion of genomic reconstruction. An algorithm for listing all maximal omnitigs was also proposed, by launching an exhaustive visit from every edge. In this paper, we prove new insights about the structure of omnitigs and solve several open questions about them. We combine these to achieve an O(nm)-time algorithm for outputting all the maximal omnitigs of a graph (with n nodes and m edges). This is also optimal, as we show families of graphs whose total omnitig length is Omega(nm). We implement this algorithm and show that it is 9-12 times faster in practice than the one of Tomescu and Medvedev [RECOMB 2016].

Cite as

Massimo Cairo, Paul Medvedev, Nidia Obscura Acosta, Romeo Rizzi, and Alexandru I. Tomescu. Optimal Omnitig Listing for Safe and Complete Contig Assembly. In 28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 78, pp. 29:1-29:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Copy BibTex To Clipboard

@InProceedings{cairo_et_al:LIPIcs.CPM.2017.29,
  author =	{Cairo, Massimo and Medvedev, Paul and Obscura Acosta, Nidia and Rizzi, Romeo and Tomescu, Alexandru I.},
  title =	{{Optimal Omnitig Listing for Safe and Complete Contig Assembly}},
  booktitle =	{28th Annual Symposium on Combinatorial Pattern Matching (CPM 2017)},
  pages =	{29:1--29:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-039-2},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{78},
  editor =	{K\"{a}rkk\"{a}inen, Juha and Radoszewski, Jakub and Rytter, Wojciech},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2017.29},
  URN =		{urn:nbn:de:0030-drops-73423},
  doi =		{10.4230/LIPIcs.CPM.2017.29},
  annote =	{Keywords: genome assembly, graph algorithm, edge-covering walk, strong bridge}
}
  • Refine by Author
  • 4 Medvedev, Paul
  • 2 Chikhi, Rayan
  • 2 Dufresne, Yoann
  • 2 Rahman, Amatur
  • 1 Cairo, Massimo
  • Show More...

  • Refine by Classification
  • 3 Applied computing → Computational biology
  • 1 Applied computing → Bioinformatics
  • 1 Applied computing → Sequencing and genotyping technologies
  • 1 Theory of computation → Design and analysis of algorithms

  • Refine by Keyword
  • 2 genome assembly
  • 2 k-mer sets
  • 2 spectrum-preserving string sets
  • 1 DNA sequencing
  • 1 Dynamic Programming
  • Show More...

  • Refine by Type
  • 6 document

  • Refine by Publication Year
  • 2 2020
  • 2 2023
  • 1 2017
  • 1 2022

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail