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2019
Conference article
Open Access
Fast dictionary-based compression for inverted indexes
Pibiri G E, Petri M, Moffat A
Dictionary-based compression schemes provide fast decoding operation, typically at the expense of reduced compression effectiveness compared to statistical or probability-based approaches. In this work, we apply dictionary-based techniques to the compression of inverted lists, showing that the high degree of regularity that these integer sequences exhibit is a good match for certain types of dictionary methods, and that an important new trade-off balance between compression effectiveness and compression efficiency can be achieved. Our observations are supported by experiments using the document-level inverted index data for two large text collections, and a wide range of other index compression implementations as reference points. Those experiments demonstrate that the gap between efficiency and effectiveness can be substantially narrowed.DOI: 10.1145/3289600.3290962
Metrics:
Pibiri G E, Petri M, Moffat A
Dictionary-based compression schemes provide fast decoding operation, typically at the expense of reduced compression effectiveness compared to statistical or probability-based approaches. In this work, we apply dictionary-based techniques to the compression of inverted lists, showing that the high degree of regularity that these integer sequences exhibit is a good match for certain types of dictionary methods, and that an important new trade-off balance between compression effectiveness and compression efficiency can be achieved. Our observations are supported by experiments using the document-level inverted index data for two large text collections, and a wide range of other index compression implementations as reference points. Those experiments demonstrate that the gap between efficiency and effectiveness can be substantially narrowed.DOI: 10.1145/3289600.3290962
Metrics:
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dl.acm.org 
| CNR IRIS | ISTI Repository | doi.org 
| CNR IRIS | CNR IRIS
2019
Other
Open Access
Space and time-efficient data structures for massive datasets
Pibiri G. M.
This thesis concerns the design of compressed data structures for the efficient storage of massive datasets of integer sequences and short strings.
Pibiri G. M.
This thesis concerns the design of compressed data structures for the efficient storage of massive datasets of integer sequences and short strings.
See at:
etd.adm.unipi.it | ISTI Repository | CNR ExploRA
2020
Journal article
Open Access
Practical trade-offs for the prefix-sum problem
Pibiri Ge, Venturini R
Given an integer arrayA, theprefix-sum problemis to answersum(i)queries that return the sum of the elements inA[0..i], knowing that the integers inAcan be changed. It is a classic problem in data structure design with a wide range of applications in computing from coding to databases. In this work, we propose and compare practical solutions to this problem, showing that new trade-offs between the performance of queries and updates can be achieved on modern hardware.Source: SOFTWARE-PRACTICE & EXPERIENCE
DOI: 10.1002/spe.2918
DOI: 10.48550/arxiv.2006.14552
Project(s): BigDataGrapes
Metrics:
Pibiri Ge, Venturini R
Given an integer arrayA, theprefix-sum problemis to answersum(i)queries that return the sum of the elements inA[0..i], knowing that the integers inAcan be changed. It is a classic problem in data structure design with a wide range of applications in computing from coding to databases. In this work, we propose and compare practical solutions to this problem, showing that new trade-offs between the performance of queries and updates can be achieved on modern hardware.Source: SOFTWARE-PRACTICE & EXPERIENCE
DOI: 10.1002/spe.2918
DOI: 10.48550/arxiv.2006.14552
Project(s): BigDataGrapes
Metrics:
See at:
arXiv.org e-Print Archive | Software Practice and Experience | CNR IRIS | onlinelibrary.wiley.com | Software Practice and Experience | doi.org | CNR IRIS
2020
Journal article
Open Access
Techniques for inverted index compression
Pibiri Ge, Venturini R
The data structure at the core of large-scale search engines is the inverted index, which is essentially a collection of sorted integer sequences called inverted lists. Because of the many documents indexed by such engines and stringent performance requirements imposed by the heavy load of queries, the inverted index stores billions of integers that must be searched efficiently. In this scenario, index compression is essential because it leads to a better exploitation of the computer memory hierarchy for faster query processing and, at the same time, allows reducing the number of storage machines. The aim of this article is twofold: first, surveying the encoding algorithms suitable for inverted index compression and, second, characterizing the performance of the inverted index through experimentation.Source: ACM COMPUTING SURVEYS, vol. 53 (issue 6)
DOI: 10.1145/3415148
DOI: 10.48550/arxiv.1908.10598
Project(s): BigDataGrapes
Metrics:
Pibiri Ge, Venturini R
The data structure at the core of large-scale search engines is the inverted index, which is essentially a collection of sorted integer sequences called inverted lists. Because of the many documents indexed by such engines and stringent performance requirements imposed by the heavy load of queries, the inverted index stores billions of integers that must be searched efficiently. In this scenario, index compression is essential because it leads to a better exploitation of the computer memory hierarchy for faster query processing and, at the same time, allows reducing the number of storage machines. The aim of this article is twofold: first, surveying the encoding algorithms suitable for inverted index compression and, second, characterizing the performance of the inverted index through experimentation.Source: ACM COMPUTING SURVEYS, vol. 53 (issue 6)
DOI: 10.1145/3415148
DOI: 10.48550/arxiv.1908.10598
Project(s): BigDataGrapes
Metrics:
See at:
arXiv.org e-Print Archive | ACM Computing Surveys | dl.acm.org | CNR IRIS | ISTI Repository | ACM Computing Surveys | doi.org | CNR IRIS | CNR IRIS
2021
Conference article
Open Access
Fast and compact set intersection through recursive universe partitioning
Pibiri Ge
We present a data structure that encodes a sorted integer sequence in small space allowing, at the same time, fast intersection operations. The data layout is carefully designed to exploit word-level parallelism and SIMD instructions, hence providing good practical performance. The core algorithmic idea is that of recursive partitioning the universe of representation: a markedly different paradigm than the widespread strategy of partitioning the sequence based on its length. Extensive experimentation and comparison against several competitive techniques shows that the proposed solution embodies an improved space/time trade-off for the set intersection problem.DOI: 10.1109/dcc50243.2021.00037
Metrics:
Pibiri Ge
We present a data structure that encodes a sorted integer sequence in small space allowing, at the same time, fast intersection operations. The data layout is carefully designed to exploit word-level parallelism and SIMD instructions, hence providing good practical performance. The core algorithmic idea is that of recursive partitioning the universe of representation: a markedly different paradigm than the widespread strategy of partitioning the sequence based on its length. Extensive experimentation and comparison against several competitive techniques shows that the proposed solution embodies an improved space/time trade-off for the set intersection problem.DOI: 10.1109/dcc50243.2021.00037
Metrics:
See at:
CNR IRIS | ieeexplore.ieee.org | ISTI Repository | doi.org | CNR IRIS | CNR IRIS
2021
Journal article
Open Access
Rank/select queries over mutable bitmaps
Pibiri Ge, Kanda S
The problem of answering rank/select queries over a bitmap is of utmost importance for many succinct data structures. When the bitmap does not change, many solutions exist in the theoretical and practical side. In this work we consider the case where one is allowed to modify the bitmap via a flip(i) operation that toggles its i-th bit. By adapting and properly extending some results concerning prefix-sum data structures, we present a practical solution to the problem, tailored for modern CPU instruction sets. Compared to the state-of-the-art, our solution improves runtime with no space degradation. Moreover, it does not incur in a significant runtime penalty when compared to the fastest immutable indexes, while providing even lower space overhead.Source: INFORMATION SYSTEMS, vol. 99 (issue 101756)
DOI: 10.1016/j.is.2021.101756
DOI: 10.48550/arxiv.2009.12809
Project(s): BigDataGrapes
Metrics:
Pibiri Ge, Kanda S
The problem of answering rank/select queries over a bitmap is of utmost importance for many succinct data structures. When the bitmap does not change, many solutions exist in the theoretical and practical side. In this work we consider the case where one is allowed to modify the bitmap via a flip(i) operation that toggles its i-th bit. By adapting and properly extending some results concerning prefix-sum data structures, we present a practical solution to the problem, tailored for modern CPU instruction sets. Compared to the state-of-the-art, our solution improves runtime with no space degradation. Moreover, it does not incur in a significant runtime penalty when compared to the fastest immutable indexes, while providing even lower space overhead.Source: INFORMATION SYSTEMS, vol. 99 (issue 101756)
DOI: 10.1016/j.is.2021.101756
DOI: 10.48550/arxiv.2009.12809
Project(s): BigDataGrapes
Metrics:
See at:
arXiv.org e-Print Archive | Information Systems | CNR IRIS | ISTI Repository | www.sciencedirect.com | Information Systems | doi.org | CNR IRIS | CNR IRIS
2022
Journal article
Open Access
Sparse and skew hashing of K-mers
Pibiri Ge
MOTIVATION: A dictionary of k-mers is a data structure that stores a set of n distinct k-mers and supports membership queries. This data structure is at the hearth of many important tasks in computational biology. High-throughput sequencing of DNA can produce very large k-mer sets, in the size of billions of strings-in such cases, the memory consumption and query efficiency of the data structure is a concrete challenge. RESULTS: To tackle this problem, we describe a compressed and associative dictionary for k-mers, that is: a data structure where strings are represented in compact form and each of them is associated to a unique integer identifier in the range [0,n). We show that some statistical properties of k-mer minimizers can be exploited by minimal perfect hashing to substantially improve the space/time trade-off of the dictionary compared to the best-known solutions. AVAILABILITY AND IMPLEMENTATION: https://github.com/jermp/sshash. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.Source: BIOINFORMATICS (OXF., ONLINE), vol. 38 (issue 1), pp. i185-i194
DOI: 10.1093/bioinformatics/btac245
Project(s): MobiDataLab
Metrics:
Pibiri Ge
MOTIVATION: A dictionary of k-mers is a data structure that stores a set of n distinct k-mers and supports membership queries. This data structure is at the hearth of many important tasks in computational biology. High-throughput sequencing of DNA can produce very large k-mer sets, in the size of billions of strings-in such cases, the memory consumption and query efficiency of the data structure is a concrete challenge. RESULTS: To tackle this problem, we describe a compressed and associative dictionary for k-mers, that is: a data structure where strings are represented in compact form and each of them is associated to a unique integer identifier in the range [0,n). We show that some statistical properties of k-mer minimizers can be exploited by minimal perfect hashing to substantially improve the space/time trade-off of the dictionary compared to the best-known solutions. AVAILABILITY AND IMPLEMENTATION: https://github.com/jermp/sshash. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.Source: BIOINFORMATICS (OXF., ONLINE), vol. 38 (issue 1), pp. i185-i194
DOI: 10.1093/bioinformatics/btac245
Project(s): MobiDataLab
Metrics:
See at:
academic.oup.com | CNR IRIS | ISTI Repository | CNR IRIS
2022
Conference article
Open Access
On weighted k-mer dictionaries
Pibiri Ge
We consider the problem of representing a set of k-mers and their abundance counts, or weights, in compressed space so that assessing membership and retrieving the weight of a k-mer is efficient. The representation is called a weighted dictionary of k-mers and finds application in numerous tasks in Bioinformatics that usually count k-mers as a pre-processing step. In fact, k-mer counting tools produce very large outputs that may result in a severe bottleneck for subsequent processing. In this work we extend the recently introduced SSHash dictionary (Pibiri, Bioinformatics 2022) to also store compactly the weights of the k-mers. From a technical perspective, we exploit the order of the k-mers represented in SSHash to encode runs of weights, hence allowing (several times) better compression than the empirical entropy of the weights. We also study the problem of reducing the number of runs in the weights to improve compression even further and illustrate a lower bound for this problem. We propose an efficient, greedy, algorithm to reduce the number of runs and show empirically that it performs well, i.e., very similarly to the lower bound. Lastly, we corroborate our findings with experiments on real-world datasets and comparison with competitive alternatives. Up to date, SSHash is the only k-mer dictionary that is exact, weighted, associative, fast, and small.Source: LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS. Potsdam, Germany, 05-09/09/2022
DOI: 10.4230/lipics.wabi.2022.9
Project(s): MobiDataLab
Metrics:
Pibiri Ge
We consider the problem of representing a set of k-mers and their abundance counts, or weights, in compressed space so that assessing membership and retrieving the weight of a k-mer is efficient. The representation is called a weighted dictionary of k-mers and finds application in numerous tasks in Bioinformatics that usually count k-mers as a pre-processing step. In fact, k-mer counting tools produce very large outputs that may result in a severe bottleneck for subsequent processing. In this work we extend the recently introduced SSHash dictionary (Pibiri, Bioinformatics 2022) to also store compactly the weights of the k-mers. From a technical perspective, we exploit the order of the k-mers represented in SSHash to encode runs of weights, hence allowing (several times) better compression than the empirical entropy of the weights. We also study the problem of reducing the number of runs in the weights to improve compression even further and illustrate a lower bound for this problem. We propose an efficient, greedy, algorithm to reduce the number of runs and show empirically that it performs well, i.e., very similarly to the lower bound. Lastly, we corroborate our findings with experiments on real-world datasets and comparison with competitive alternatives. Up to date, SSHash is the only k-mer dictionary that is exact, weighted, associative, fast, and small.Source: LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS. Potsdam, Germany, 05-09/09/2022
DOI: 10.4230/lipics.wabi.2022.9
Project(s): MobiDataLab
Metrics:
See at:
drops.dagstuhl.de | CNR IRIS | ISTI Repository | CNR IRIS
2023
Conference article
Open Access
Spectrum preserving tilings enable sparse and modular reference indexing
Fan J, Khan J, Pibiri Ge, Patro R
The reference indexing problem for -mers is to pre-process a collection of reference genomic sequences so that the position of all occurrences of any queried -mer can be rapidly identified. An efficient and scalable solution to this problem is fundamental for many tasks in bioinformatics. In this work, we introduce the spectrum preserving tiling (SPT), a general representation of that specifies how a set of tiles repeatedly occur to spell out the constituent reference sequences in. By encoding the order and positions where tiles occur, SPTs enable the implementation and analysis of a general class of modular indexes. An index over an SPT decomposes the reference indexing problem for -mers into: (1) a -mer-to-tile mapping; and (2) a tile-to-occurrence mapping. Recently introduced work to construct and compactly index -mer sets can be used to efficiently implement the -mer-to-tile mapping. However, implementing the tile-to-occurrence mapping remains prohibitively costly in terms of space. As reference collections become large, the space requirements of the tile-to-occurrence mapping dominates that of the -mer-to-tile mapping since the former depends on the amount of total sequence while the latter depends on the number of unique -mers in. To address this, we introduce a class of sampling schemes for SPTs that trade off speed to reduce the size of the tile-to-reference mapping. We implement a practical index with these sampling schemes in the tool pufferfish2. When indexing over 30,000 bacterial genomes, pufferfish2 reduces the size of the tile-to-occurrence mapping from 86.3 GB to 34.6 GB while incurring only a 3.6 slowdown when querying -mers from a sequenced readset. Availability: pufferfish2 is implemented in Rust and available at https://github.com/COMBINE-lab/pufferfish2.DOI: 10.1007/978-3-031-29119-7_2
Project(s): MobiDataLab
Metrics:
Fan J, Khan J, Pibiri Ge, Patro R
The reference indexing problem for -mers is to pre-process a collection of reference genomic sequences so that the position of all occurrences of any queried -mer can be rapidly identified. An efficient and scalable solution to this problem is fundamental for many tasks in bioinformatics. In this work, we introduce the spectrum preserving tiling (SPT), a general representation of that specifies how a set of tiles repeatedly occur to spell out the constituent reference sequences in. By encoding the order and positions where tiles occur, SPTs enable the implementation and analysis of a general class of modular indexes. An index over an SPT decomposes the reference indexing problem for -mers into: (1) a -mer-to-tile mapping; and (2) a tile-to-occurrence mapping. Recently introduced work to construct and compactly index -mer sets can be used to efficiently implement the -mer-to-tile mapping. However, implementing the tile-to-occurrence mapping remains prohibitively costly in terms of space. As reference collections become large, the space requirements of the tile-to-occurrence mapping dominates that of the -mer-to-tile mapping since the former depends on the amount of total sequence while the latter depends on the number of unique -mers in. To address this, we introduce a class of sampling schemes for SPTs that trade off speed to reduce the size of the tile-to-reference mapping. We implement a practical index with these sampling schemes in the tool pufferfish2. When indexing over 30,000 bacterial genomes, pufferfish2 reduces the size of the tile-to-occurrence mapping from 86.3 GB to 34.6 GB while incurring only a 3.6 slowdown when querying -mers from a sequenced readset. Availability: pufferfish2 is implemented in Rust and available at https://github.com/COMBINE-lab/pufferfish2.DOI: 10.1007/978-3-031-29119-7_2
Project(s): MobiDataLab
Metrics:
See at:
CNR IRIS | link.springer.com | ISTI Repository | CNR IRIS
2023
Journal article
Open Access
On weighted k-mer dictionaries
Pibiri Ge
We consider the problem of representing a set of k-mers and their abundance counts, or weights, in compressed space so that assessing membership and retrieving the weight of a k-mer is efficient. The representation is called a weighted dictionary of k-mers and finds application in numerous tasks in Bioinformatics that usually count k-mers as a pre-processing step. In fact, k-mer counting tools produce very large outputs that may result in a severe bottleneck for subsequent processing. In this work we extend the recently introduced SSHash dictionary (Pibiri in Bioinformatics 38:185-194, 2022) to also store compactly the weights of the k-mers. From a technical perspective, we exploit the order of the k-mers represented in SSHash to encode runs of weights, hence allowing much better compression than the empirical entropy of the weights. We study the problem of reducing the number of runs in the weights to improve compression even further and give an optimal algorithm for this problem. Lastly, we corroborate our findings with experiments on real-world datasets and comparison with competitive alternatives. Up to date, SSHash is the only k-mer dictionary that is exact, weighted, associative, fast, and small.Source: ALGORITHMS FOR MOLECULAR BIOLOGY, vol. 18 (issue 1)
DOI: 10.1186/s13015-023-00226-2
Metrics:
Pibiri Ge
We consider the problem of representing a set of k-mers and their abundance counts, or weights, in compressed space so that assessing membership and retrieving the weight of a k-mer is efficient. The representation is called a weighted dictionary of k-mers and finds application in numerous tasks in Bioinformatics that usually count k-mers as a pre-processing step. In fact, k-mer counting tools produce very large outputs that may result in a severe bottleneck for subsequent processing. In this work we extend the recently introduced SSHash dictionary (Pibiri in Bioinformatics 38:185-194, 2022) to also store compactly the weights of the k-mers. From a technical perspective, we exploit the order of the k-mers represented in SSHash to encode runs of weights, hence allowing much better compression than the empirical entropy of the weights. We study the problem of reducing the number of runs in the weights to improve compression even further and give an optimal algorithm for this problem. Lastly, we corroborate our findings with experiments on real-world datasets and comparison with competitive alternatives. Up to date, SSHash is the only k-mer dictionary that is exact, weighted, associative, fast, and small.Source: ALGORITHMS FOR MOLECULAR BIOLOGY, vol. 18 (issue 1)
DOI: 10.1186/s13015-023-00226-2
Metrics:
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almob.biomedcentral.com | CNR IRIS | ISTI Repository | CNR IRIS
2023
Journal article
Open Access
Matchtigs: minimum plain text representation of k-mer sets
Schmidt S, Khan S, Alanko Jn, Pibiri Ge, Tomescu Ai
We propose a polynomial algorithm computing a minimum plain-text representation of k-mer sets, as well as an efficient near-minimum greedy heuristic. When compressing read sets of large model organisms or bacterial pangenomes, with only a minor runtime increase, we shrink the representation by up to 59% over unitigs and 26% over previous work. Additionally, the number of strings is decreased by up to 97% over unitigs and 90% over previous work. Finally, a small representation has advantages in downstream applications, as it speeds up SSHash-Lite queries by up to 4.26× over unitigs and 2.10× over previous work.Source: GENOME BIOLOGY (ONLINE), vol. 24
DOI: 10.1186/s13059-023-02968-z
Project(s): MobiDataLab, SAFEBIO
Metrics:
Schmidt S, Khan S, Alanko Jn, Pibiri Ge, Tomescu Ai
We propose a polynomial algorithm computing a minimum plain-text representation of k-mer sets, as well as an efficient near-minimum greedy heuristic. When compressing read sets of large model organisms or bacterial pangenomes, with only a minor runtime increase, we shrink the representation by up to 59% over unitigs and 26% over previous work. Additionally, the number of strings is decreased by up to 97% over unitigs and 90% over previous work. Finally, a small representation has advantages in downstream applications, as it speeds up SSHash-Lite queries by up to 4.26× over unitigs and 2.10× over previous work.Source: GENOME BIOLOGY (ONLINE), vol. 24
DOI: 10.1186/s13059-023-02968-z
Project(s): MobiDataLab
, SAFEBIO Metrics:
See at:
genomebiology.biomedcentral.com | CNR IRIS | ISTI Repository | CNR IRIS
2023
Journal article
Open Access
Locality-preserving minimal perfect hashing of k-mers
Pibiri Ge, Shibuya Y, Limasset A
Motivation: Minimal perfect hashing is the problem of mapping a static set of n distinct keys into the address space {1, ... , n} bijectively. It is well-known that n log2(e) bits are necessary to specify a minimal perfect hash function (MPHF) f, when no additional knowledge of the input keys is to be used. However, it is often the case in practice that the input keys have intrinsic relationships that we can exploit to lower the bit complexity of f. For example, consider a string and the set of all its distinct k-mers as input keys: since two consecutive k-mers share an overlap of k - 1 symbols, it seems possible to beat the classic log2(e) bits/key barrier in this case. Moreover, we would like f to map consecutive k-mers to consecutive addresses, as to also preserve as much as possible their relationship in the codomain. This is a useful feature in practice as it guarantees a certain degree of locality of reference for f, resulting in a better evaluation time when querying consecutive k-mers.Results: Motivated by these premises, we initiate the study of a new type of locality-preserving MPHF designed for k-mers extracted consecutively from a collection of strings. We design a construction whose space usage decreases for growing k and discuss experiments with a practical implementation of the method: in practice, the functions built with our method can be several times smaller and even faster to query than the most efficient MPHFs in the literature.Code Availability: https://github.com/jermp/lphashData Availability: https://zenodo.org/record/7239205Source: BIOINFORMATICS (OXF., ONLINE), vol. 39
DOI: 10.1093/bioinformatics/btad219
Metrics:
Pibiri Ge, Shibuya Y, Limasset A
Motivation: Minimal perfect hashing is the problem of mapping a static set of n distinct keys into the address space {1, ... , n} bijectively. It is well-known that n log2(e) bits are necessary to specify a minimal perfect hash function (MPHF) f, when no additional knowledge of the input keys is to be used. However, it is often the case in practice that the input keys have intrinsic relationships that we can exploit to lower the bit complexity of f. For example, consider a string and the set of all its distinct k-mers as input keys: since two consecutive k-mers share an overlap of k - 1 symbols, it seems possible to beat the classic log2(e) bits/key barrier in this case. Moreover, we would like f to map consecutive k-mers to consecutive addresses, as to also preserve as much as possible their relationship in the codomain. This is a useful feature in practice as it guarantees a certain degree of locality of reference for f, resulting in a better evaluation time when querying consecutive k-mers.Results: Motivated by these premises, we initiate the study of a new type of locality-preserving MPHF designed for k-mers extracted consecutively from a collection of strings. We design a construction whose space usage decreases for growing k and discuss experiments with a practical implementation of the method: in practice, the functions built with our method can be several times smaller and even faster to query than the most efficient MPHFs in the literature.Code Availability: https://github.com/jermp/lphashData Availability: https://zenodo.org/record/7239205Source: BIOINFORMATICS (OXF., ONLINE), vol. 39
DOI: 10.1093/bioinformatics/btad219
Metrics:
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academic.oup.com | CNR IRIS | ISTI Repository | ISTI Repository | CNR IRIS | CNR IRIS
2023
Conference article
Open Access
Fulgor: a fast and compact {k-mer} index for large-scale matching and color queries
Fan J, Singh Np, Khan J, Pibiri Ge, Patro R
The problem of sequence identification or matching - determining the subset of reference sequences from a given collection that are likely to contain a short, queried nucleotide sequence - is relevant for many important tasks in Computational Biology, such as metagenomics and pan-genome analysis. Due to the complex nature of such analyses and the large scale of the reference collections a resource-efficient solution to this problem is of utmost importance. This poses the threefold challenge of representing the reference collection with a data structure that is efficient to query, has light memory usage, and scales well to large collections. To solve this problem, we describe how recent advancements in associative, order-preserving, k-mer dictionaries can be combined with a compressed inverted index to implement a fast and compact colored de Bruijn graph data structure. This index takes full advantage of the fact that unitigs in the colored de Bruijn graph are monochromatic (all k-mers in a unitig have the same set of references of origin, or "color"), leveraging the order-preserving property of its dictionary. In fact, k-mers are kept in unitig order by the dictionary, thereby allowing for the encoding of the map from k-mers to their inverted lists in as little as 1+o(1) bits per unitig. Hence, one inverted list per unitig is stored in the index with almost no space/time overhead. By combining this property with simple but effective compression methods for inverted lists, the index achieves very small space. We implement these methods in a tool called Fulgor. Compared to Themisto, the prior state of the art, Fulgor indexes a heterogeneous collection of 30,691 bacterial genomes in 3.8× less space, a collection of 150,000 Salmonella enterica genomes in approximately 2× less space, is at least twice as fast for color queries, and is 2-6 × faster to construct.Source: LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS, pp. 18:1-18:21. Houston, Texas (USA), 03-06/09/2023
DOI: 10.4230/lipics.wabi.2023.18
DOI: 10.1101/2023.05.09.539895
Metrics:
Fan J, Singh Np, Khan J, Pibiri Ge, Patro R
The problem of sequence identification or matching - determining the subset of reference sequences from a given collection that are likely to contain a short, queried nucleotide sequence - is relevant for many important tasks in Computational Biology, such as metagenomics and pan-genome analysis. Due to the complex nature of such analyses and the large scale of the reference collections a resource-efficient solution to this problem is of utmost importance. This poses the threefold challenge of representing the reference collection with a data structure that is efficient to query, has light memory usage, and scales well to large collections. To solve this problem, we describe how recent advancements in associative, order-preserving, k-mer dictionaries can be combined with a compressed inverted index to implement a fast and compact colored de Bruijn graph data structure. This index takes full advantage of the fact that unitigs in the colored de Bruijn graph are monochromatic (all k-mers in a unitig have the same set of references of origin, or "color"), leveraging the order-preserving property of its dictionary. In fact, k-mers are kept in unitig order by the dictionary, thereby allowing for the encoding of the map from k-mers to their inverted lists in as little as 1+o(1) bits per unitig. Hence, one inverted list per unitig is stored in the index with almost no space/time overhead. By combining this property with simple but effective compression methods for inverted lists, the index achieves very small space. We implement these methods in a tool called Fulgor. Compared to Themisto, the prior state of the art, Fulgor indexes a heterogeneous collection of 30,691 bacterial genomes in 3.8× less space, a collection of 150,000 Salmonella enterica genomes in approximately 2× less space, is at least twice as fast for color queries, and is 2-6 × faster to construct.Source: LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS, pp. 18:1-18:21. Houston, Texas (USA), 03-06/09/2023
DOI: 10.4230/lipics.wabi.2023.18
DOI: 10.1101/2023.05.09.539895
Metrics:
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drops.dagstuhl.de | Europe PubMed Central | Archivio istituzionale della ricerca - Università degli Studi di Venezia Ca' Foscari | CNR IRIS | doi.org | doi.org | CNR IRIS | pubmed.ncbi.nlm.nih.gov
2024
Journal article
Open Access
Fulgor: a fast and compact k-mer index for large-scale matching and color queries
Fan J, Khan J, Pratap Singh N, Pibiri Ge, Patro R
The problem of sequence identification or matching--determining the subset of reference sequences from a givencollection that are likely to contain a short, queried nucleotide sequence--is relevant for many important tasksin Computational Biology, such as metagenomics and pangenome analysis. Due to the complex nature of such analysesand the large scale of the reference collections a resource-efficient solution to this problem is of utmost importance.This poses the threefold challenge of representing the reference collection with a data structure that is efficientto query, has light memory usage, and scales well to large collections. To solve this problem, we describe an efficientcolored de Bruijn graph index, arising as the combination of a k-mer dictionary with a compressed inverted index. Theproposed index takes full advantage of the fact that unitigs in the colored compacted de Bruijn graph are monochromatic(i.e., all k-mers in a unitig have the same set of references of origin, or color). Specifically, the unitigs are keptin the dictionary in color order, thereby allowing for the encoding of the map from k-mers to their colors in as littleas 1 + o(1) bits per unitig. Hence, one color per unitig is stored in the index with almost no space/time overhead. Bycombining this property with simple but effective compression methods for integer lists, the index achieves verysmall space. We implement these methods in a tool called Fulgor, and conduct an extensive experimental analysisto demonstrate the improvement of our tool over previous solutions. For example, compared to Themisto--thestrongest competitor in terms of index space vs. query time trade-off--Fulgor requires significantly less space (upto 43% less space for a collection of 150,000 Salmonella enterica genomes), is at least twice as fast for color queries,and is 2-6× faster to construct.Source: ALGORITHMS FOR MOLECULAR BIOLOGY, vol. 19 (issue 3)
DOI: 10.1186/s13015-024-00251-9
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Fan J, Khan J, Pratap Singh N, Pibiri Ge, Patro R
The problem of sequence identification or matching--determining the subset of reference sequences from a givencollection that are likely to contain a short, queried nucleotide sequence--is relevant for many important tasksin Computational Biology, such as metagenomics and pangenome analysis. Due to the complex nature of such analysesand the large scale of the reference collections a resource-efficient solution to this problem is of utmost importance.This poses the threefold challenge of representing the reference collection with a data structure that is efficientto query, has light memory usage, and scales well to large collections. To solve this problem, we describe an efficientcolored de Bruijn graph index, arising as the combination of a k-mer dictionary with a compressed inverted index. Theproposed index takes full advantage of the fact that unitigs in the colored compacted de Bruijn graph are monochromatic(i.e., all k-mers in a unitig have the same set of references of origin, or color). Specifically, the unitigs are keptin the dictionary in color order, thereby allowing for the encoding of the map from k-mers to their colors in as littleas 1 + o(1) bits per unitig. Hence, one color per unitig is stored in the index with almost no space/time overhead. Bycombining this property with simple but effective compression methods for integer lists, the index achieves verysmall space. We implement these methods in a tool called Fulgor, and conduct an extensive experimental analysisto demonstrate the improvement of our tool over previous solutions. For example, compared to Themisto--thestrongest competitor in terms of index space vs. query time trade-off--Fulgor requires significantly less space (upto 43% less space for a collection of 150,000 Salmonella enterica genomes), is at least twice as fast for color queries,and is 2-6× faster to construct.Source: ALGORITHMS FOR MOLECULAR BIOLOGY, vol. 19 (issue 3)
DOI: 10.1186/s13015-024-00251-9
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almob.biomedcentral.com | CNR IRIS | ISTI Repository | CNR IRIS
2024
Conference article
Open Access
The {mod-minimizer}: a simple and efficient sampling algorithm for long k-Mers
Koerkamp R. G., Pibiri G. E.
Motivation. Given a string S, a minimizer scheme is an algorithm defined by a triple (k,w,O) that samples a subset of k-mers (k-long substrings) from a string S. Specifically, it samples the smallest k-mer according to the order O from each window of w consecutive k-mers in S. Because consecutive windows can sample the same k-mer, the set of the sampled k-mers is typically much smaller than S. More generally, we consider substring sampling algorithms that respect a window guarantee: at least one k-mer must be sampled from every window of w consecutive k-mers. As a sampled k-mer is uniquely identified by its absolute position in S, we can define the density of a sampling algorithm as the fraction of distinct sampled positions. Good methods have low density which, by respecting the window guarantee, is lower bounded by 1/w. It is however difficult to design a sequence-agnostic algorithm with provably optimal density. In practice, the order O is usually implemented using a pseudo-random hash function to obtain the so-called random minimizer. This scheme is simple to implement, very fast to compute even in streaming fashion, and easy to analyze. However, its density is almost a factor of 2 away from the lower bound for large windows. Methods. In this work we introduce mod-sampling, a two-step sampling algorithm to obtain new minimizer schemes. Given a (small) parameter t, the mod-sampling algorithm finds the position p of the smallest t-mer in a window. It then samples the k-mer at position pod w. The lr-minimizer uses t = k-w and the mod-minimizer uses t≡ k (mod w). Results. These new schemes have provably lower density than random minimizers and other schemes when k is large compared to w, while being as fast to compute. Importantly, the mod-minimizer achieves optimal density when k → ∞. Although the mod-minimizer is not the first method to achieve optimal density for large k, its proof of optimality is simpler than previous work. We provide pseudocode for a number of other methods and compare to them. In practice, the mod-minimizer has considerably lower density than the random minimizer and other state-of-the-art methods, like closed syncmers and miniception, when k > w. We plugged the mod-minimizer into SSHash, a k-mer dictionary based on minimizers. For default parameters (w,k) = (11,21), space usage decreases by 15% when indexing the whole human genome (GRCh38), while maintaining its fast query time.Source: LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS, vol. 312. Royal Holloway, London, United Kingdom, 2-4/09/2024
DOI: 10.4230/lipics.wabi.2024.11
Metrics:
Koerkamp R. G., Pibiri G. E.
Motivation. Given a string S, a minimizer scheme is an algorithm defined by a triple (k,w,O) that samples a subset of k-mers (k-long substrings) from a string S. Specifically, it samples the smallest k-mer according to the order O from each window of w consecutive k-mers in S. Because consecutive windows can sample the same k-mer, the set of the sampled k-mers is typically much smaller than S. More generally, we consider substring sampling algorithms that respect a window guarantee: at least one k-mer must be sampled from every window of w consecutive k-mers. As a sampled k-mer is uniquely identified by its absolute position in S, we can define the density of a sampling algorithm as the fraction of distinct sampled positions. Good methods have low density which, by respecting the window guarantee, is lower bounded by 1/w. It is however difficult to design a sequence-agnostic algorithm with provably optimal density. In practice, the order O is usually implemented using a pseudo-random hash function to obtain the so-called random minimizer. This scheme is simple to implement, very fast to compute even in streaming fashion, and easy to analyze. However, its density is almost a factor of 2 away from the lower bound for large windows. Methods. In this work we introduce mod-sampling, a two-step sampling algorithm to obtain new minimizer schemes. Given a (small) parameter t, the mod-sampling algorithm finds the position p of the smallest t-mer in a window. It then samples the k-mer at position pod w. The lr-minimizer uses t = k-w and the mod-minimizer uses t≡ k (mod w). Results. These new schemes have provably lower density than random minimizers and other schemes when k is large compared to w, while being as fast to compute. Importantly, the mod-minimizer achieves optimal density when k → ∞. Although the mod-minimizer is not the first method to achieve optimal density for large k, its proof of optimality is simpler than previous work. We provide pseudocode for a number of other methods and compare to them. In practice, the mod-minimizer has considerably lower density than the random minimizer and other state-of-the-art methods, like closed syncmers and miniception, when k > w. We plugged the mod-minimizer into SSHash, a k-mer dictionary based on minimizers. For default parameters (w,k) = (11,21), space usage decreases by 15% when indexing the whole human genome (GRCh38), while maintaining its fast query time.Source: LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS, vol. 312. Royal Holloway, London, United Kingdom, 2-4/09/2024
DOI: 10.4230/lipics.wabi.2024.11
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2024
Journal article
Open Access
Where the patterns are: repetition-aware compression for colored de Bruijn graphs
Campanelli A., Pibiri G. E., Fan J., Patro R.
We describe lossless compressed data structures for the colored de Bruijn graph (or c-dBG). Given a collection of reference sequences, a c-dBG can be essentially regarded as a map from k-mers to their color sets. The color set of a k-mer is the set of all identifiers, or colors, of the references that contain the k-mer. While these maps find countless applications in computational biology (e.g., basic query, reading mapping, abundance estimation, etc.), their memory usage represents a serious challenge for large-scale sequence indexing. Our solutions leverage on the intrinsic repetitiveness of the color sets when indexing large collections of related genomes. Hence, the described algorithms factorize the color sets into patterns that repeat across the entire collection and represent these patterns once instead of redundantly replicating their representation as would happen if the sets were encoded as atomic lists of integers. Experimental results across a range of datasets and query workloads show that these representations substantially improve over the space effectiveness of the best previous solutions (sometimes, even dramatically, yielding indexes that are smaller by an order of magnitude). Despite the space reduction, these indexes only moderately impact the efficiency of the queries compared to the fastest indexes.Source: JOURNAL OF COMPUTATIONAL BIOLOGY
DOI: 10.1089/cmb.2024.0714
DOI: 10.1101/2024.07.09.602727
Project(s): EFRA
Metrics:
Campanelli A., Pibiri G. E., Fan J., Patro R.
We describe lossless compressed data structures for the colored de Bruijn graph (or c-dBG). Given a collection of reference sequences, a c-dBG can be essentially regarded as a map from k-mers to their color sets. The color set of a k-mer is the set of all identifiers, or colors, of the references that contain the k-mer. While these maps find countless applications in computational biology (e.g., basic query, reading mapping, abundance estimation, etc.), their memory usage represents a serious challenge for large-scale sequence indexing. Our solutions leverage on the intrinsic repetitiveness of the color sets when indexing large collections of related genomes. Hence, the described algorithms factorize the color sets into patterns that repeat across the entire collection and represent these patterns once instead of redundantly replicating their representation as would happen if the sets were encoded as atomic lists of integers. Experimental results across a range of datasets and query workloads show that these representations substantially improve over the space effectiveness of the best previous solutions (sometimes, even dramatically, yielding indexes that are smaller by an order of magnitude). Despite the space reduction, these indexes only moderately impact the efficiency of the queries compared to the fastest indexes.Source: JOURNAL OF COMPUTATIONAL BIOLOGY
DOI: 10.1089/cmb.2024.0714
DOI: 10.1101/2024.07.09.602727
Project(s): EFRA
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Archivio istituzionale della ricerca - Università degli Studi di Venezia Ca' Foscari | Archivio istituzionale della ricerca - Università degli Studi di Venezia Ca' Foscari | IRIS Cnr | IRIS Cnr | Journal of Computational Biology | doi.org | CNR IRIS | CNR IRIS
2023
Conference article
Open Access
Verifiable learning for robust tree ensembles
Calzavara S., Cazzaro L., Pibiri G. E., Prezza N.
Verifying the robustness of machine learning models against evasion attacks at test time is an important research problem. Unfortunately, prior work established that this problem is NP-hard for decision tree ensembles, hence bound to be intractable for specific inputs. In this paper, we identify a restricted class of decision tree ensembles, called large-spread ensembles, which admit a security verification algorithm running in polynomial time. We then propose a new approach called verifiable learning, which advocates the training of such restricted model classes which are amenable for efficient verification. We show the benefits of this idea by designing a new training algorithm that automatically learns a large-spread decision tree ensemble from labelled data, thus enabling its security verification in polynomial time. Experimental results on publicly available datasets confirm that large-spread ensembles trained using our algorithm can be verified in a matter of seconds, using standard commercial hardware. Moreover, large-spread ensembles are more robust than traditional ensembles against evasion attacks, while incurring in just a relatively small loss of accuracy in the non-adversarial setting.DOI: 10.1145/3576915.3623100
DOI: 10.48550/arxiv.2305.03626
Project(s): EFRA
Metrics:
Calzavara S., Cazzaro L., Pibiri G. E., Prezza N.
Verifying the robustness of machine learning models against evasion attacks at test time is an important research problem. Unfortunately, prior work established that this problem is NP-hard for decision tree ensembles, hence bound to be intractable for specific inputs. In this paper, we identify a restricted class of decision tree ensembles, called large-spread ensembles, which admit a security verification algorithm running in polynomial time. We then propose a new approach called verifiable learning, which advocates the training of such restricted model classes which are amenable for efficient verification. We show the benefits of this idea by designing a new training algorithm that automatically learns a large-spread decision tree ensemble from labelled data, thus enabling its security verification in polynomial time. Experimental results on publicly available datasets confirm that large-spread ensembles trained using our algorithm can be verified in a matter of seconds, using standard commercial hardware. Moreover, large-spread ensembles are more robust than traditional ensembles against evasion attacks, while incurring in just a relatively small loss of accuracy in the non-adversarial setting.DOI: 10.1145/3576915.3623100
DOI: 10.48550/arxiv.2305.03626
Project(s): EFRA
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arXiv.org e-Print Archive | Archivio istituzionale della ricerca - Università degli Studi di Venezia Ca' Foscari | Archivio istituzionale della ricerca - Università degli Studi di Venezia Ca' Foscari | CNR IRIS | doi.org | CNR IRIS
2017
Journal article
Open Access
Clustered Elias-Fano Indexes
Pibiri Ge, Venturini R
In this article, we propose a new index representation based on clustering the collection of posting lists and, for each created cluster, building an ad hoc reference list with respect to which all lists in the cluster are encoded with Elias-Fano. We describe a posting lists clustering algorithm tailored for our encoder and two methods for building the reference list for a cluster. Both approaches are heuristic and differ in the way postings are added to the reference list: according to their frequency in the cluster or according to the number of bits necessary for their representation.Source: ACM TRANSACTIONS ON INFORMATION SYSTEMS, vol. 36 (issue 1)
DOI: 10.1145/3052773
Project(s): SoBigData
Metrics:
Pibiri Ge, Venturini R
In this article, we propose a new index representation based on clustering the collection of posting lists and, for each created cluster, building an ad hoc reference list with respect to which all lists in the cluster are encoded with Elias-Fano. We describe a posting lists clustering algorithm tailored for our encoder and two methods for building the reference list for a cluster. Both approaches are heuristic and differ in the way postings are added to the reference list: according to their frequency in the cluster or according to the number of bits necessary for their representation.Source: ACM TRANSACTIONS ON INFORMATION SYSTEMS, vol. 36 (issue 1)
DOI: 10.1145/3052773
Project(s): SoBigData
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ACM Transactions on Information Systems | dl.acm.org | CNR IRIS | ISTI Repository | ACM Transactions on Information Systems | CNR IRIS | CNR IRIS
2017
Conference article
Open Access
Dynamic Elias-Fano Representation
Pibiri G E, Venturini R
We show that it is possible to store a dynamic ordered set S(n,u) of n integers drawn from a bounded universe of size u in space close to the information-theoretic lower bound and yet preserve the asymptotic time optimality of the operations. Our results leverage on the Elias-Fano representation of S(n,u) which takes EF(S(n,u))=n?log(u/n)?+2n bits of space and can be shown to be less than half a bit per element away from the information-theoretic minimum. Considering a RAM model with memory words of ?(log u) bits, we focus on the case in which the integers of S are drawn from a polynomial universe of size u=n?, for any ?=?(1). We represent S(n,u) with EF(S(n,u))+o(n) bits of space and: 1. support static predecessor/successor queries in O(min{1+log(u/n),loglog n}); 2. make S grow in an append-only fashion by spending O(1) per inserted element; 3. support random access in O(log n/loglog n) worst-case, insertions/deletions in O(log n/loglog n) amortized and predecessor/successor queries in O(min{1+log(u/n),loglog n}) worst-case time. These time bounds are optimal.DOI: 10.4230/lipics.cpm.2017.30
Metrics:
Pibiri G E, Venturini R
We show that it is possible to store a dynamic ordered set S(n,u) of n integers drawn from a bounded universe of size u in space close to the information-theoretic lower bound and yet preserve the asymptotic time optimality of the operations. Our results leverage on the Elias-Fano representation of S(n,u) which takes EF(S(n,u))=n?log(u/n)?+2n bits of space and can be shown to be less than half a bit per element away from the information-theoretic minimum. Considering a RAM model with memory words of ?(log u) bits, we focus on the case in which the integers of S are drawn from a polynomial universe of size u=n?, for any ?=?(1). We represent S(n,u) with EF(S(n,u))+o(n) bits of space and: 1. support static predecessor/successor queries in O(min{1+log(u/n),loglog n}); 2. make S grow in an append-only fashion by spending O(1) per inserted element; 3. support random access in O(log n/loglog n) worst-case, insertions/deletions in O(log n/loglog n) amortized and predecessor/successor queries in O(min{1+log(u/n),loglog n}) worst-case time. These time bounds are optimal.DOI: 10.4230/lipics.cpm.2017.30
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2017
Conference article
Restricted
Efficient Data Structures for Massive N-Gram Datasets
Pibiri G E, Venturini R
The effcient indexing of large and sparse N-gram datasets is crucial in several applications in Information Retrieval, Natural Language Processing and Machine Learning. Because of the stringent efficiency requirements, dealing with billions of N-grams poses the challenge of introducing a compressed representation that preserves the query processing speed. In this paperwe study the problem of reducing the space required by the representation of such datasets, maintaining the capability of looking up for a given N-gram within micro seconds. For this purpose we describe compressed, exact and lossless data structures that achieve, at the same time, high space reductions and no time degradation with respect to state-of-The-Art software packages. In particular, we present a trie data structure in which each word following a context of fixed length k, i.e., its preceding k words, is encoded as an integer whose value is proportional to the number of words that follow such context. Since the number of words following a given context is typically very small in natural languages, we are able to lower the space of representation to compression levels that were never achieved before. Despite the significant savings in space, we show that our technique introduces a negligible penalty at query time.DOI: 10.1145/3077136.3080798
Metrics:
Pibiri G E, Venturini R
The effcient indexing of large and sparse N-gram datasets is crucial in several applications in Information Retrieval, Natural Language Processing and Machine Learning. Because of the stringent efficiency requirements, dealing with billions of N-grams poses the challenge of introducing a compressed representation that preserves the query processing speed. In this paperwe study the problem of reducing the space required by the representation of such datasets, maintaining the capability of looking up for a given N-gram within micro seconds. For this purpose we describe compressed, exact and lossless data structures that achieve, at the same time, high space reductions and no time degradation with respect to state-of-The-Art software packages. In particular, we present a trie data structure in which each word following a context of fixed length k, i.e., its preceding k words, is encoded as an integer whose value is proportional to the number of words that follow such context. Since the number of words following a given context is typically very small in natural languages, we are able to lower the space of representation to compression levels that were never achieved before. Despite the significant savings in space, we show that our technique introduces a negligible penalty at query time.DOI: 10.1145/3077136.3080798
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dl.acm.org | doi.org | CNR IRIS | CNR IRIS