Smaller Fully-Functional Bidirectional BWT Indexes

Belazzougui, Djamal; Cunial, Fabio

doi:10.1007/978-3-030-59212-7_4

Cited by 3 publications

(6 citation statements)

References 51 publications

(77 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Belazzougui et al [29] showed that using a representation of the bidirectional BWT of the input string y of length n, MAW(y) can be computed in O(n + |MAW(y)|) time. Although the construction time for the representation of the bidirectional BWT was not given in [29], it was later shown by Belazzougui and Cunial [30] that the bidirectional BWT of a given string y over an integer alphabet can be incrementally constructed in O(n) time.…”

Section: Other Efficient Algorithms For Computing Mawsmentioning

confidence: 99%

Linear-time computation of DAWGs, symmetric indexing structures, and MAWs for integer alphabets

Fujishige¹,

Tsujimaru²,

Inenaga³

et al. 2023

Theoretical Computer Science

View full text Add to dashboard Cite

Section: Other Efficient Algorithms For Computing Mawsmentioning

confidence: 99%

Linear-time computation of DAWGs, symmetric indexing structures, and MAWs for integer alphabets

Fujishige¹,

Tsujimaru²,

Inenaga³

et al. 2023

Theoretical Computer Science

View full text Add to dashboard Cite

“…Proof. The forward direction: It is immediate from Lemma S2 that any occurrence (S, i, j) of R satisfies: (1) it is of the whole string that is abundant or (2) it is stratifying or (3) relatively stratifying in some other maximal repeats. ( 2) is already the condition to be found.…”

Section: Two Suffix Trees Approachmentioning

confidence: 99%

“…Another potential contribution of a Pro k rustean graph in assembly is in advancing existing assemblers with the so-called variable-order scheme. Choosing a proper k in Strategy in Algorithm 2 allows a multi- k approach, extending the functionality of variable-order de Bruijn graphs in [6] and [4]. These previous implementations have trade-offs around space-efficiency, usable k range, and the utilization of k -mer frequencies.…”

Section: Applicationmentioning

confidence: 99%

“…Determining a k for assembly is particularly crucial in de novo approaches [13] but still relies on heuristic methods [7,19]. Furthermore, creating multi-k de Bruijn graphs did not show a clear progress [3,9,23]. These "variable-order" approaches implemented a "k change" functionality to navigate the vast representations of de Bruijn graphs built with multiple k values.…”

Section: Introductionmentioning

confidence: 99%

“…suffix trees/arrays, BWT, FM-indexes, and others, are built on similar substring representations, characterized by the LCP array. Their support for string pattern queries, preserving lossless information of substrings, can be interpreted as storing k-mers of any sizes intact, making their applications to k-mer-related tasks appealing [4,9,1]. However, the main unsolvable issue is that the computational cost strictly increases with the queried k sizes, as is obvious in "order changes" in multi-k de Bruijn graphs [4].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Prokrustean Graph: A substring index for rapid k-mer size analysis

Park,

Koslicki

2023

Preprint

View full text Add to dashboard Cite

Despite the widespread adoption ofk-mer-based methods in bioinformatics, a fundamental question persists: How to elucidate the structural transition of ak-mer set when the order switches tok′? Attaining a generalized answer has significant implications tok-mer-based methods where the influence ofkhave been empirically analyzed (eg. in areas of assembly, genome comparison, etc.).We unravel the problem with a principle:k-mers andk′-mers can be grouped by their co-occurrences, and those in the same group behave similarly regardless of applications. This concept is embodied in a model, the Prokrustean graph, which embraces all similarity information of a given sequence set and has a channel to accessk-mers of anyk. This gives us a theoretical framework in which we can understand the presence and frequency ofk-mers askchanges.Practically, a Prokrustean graph is a space efficient data structure that can quickly be queried to extract essentially arbitrary information regardingk-mers with time complexity independent ofk-mer size range. We provide a series of examples that perform in competitive time and space when compared to purpose-built tools that operate on a singlek, such as KMC and GGCAT. For example, with large read sets, we can count allk-mers fork= 30 … 150 in ≃ 30 seconds in comparison to KMC requiring ≃ 30 seconds for a singlek. Similarly, on long read sets, we can count all unitigs in ≃ 30 seconds for the entire rangek= 30 …50000, a task that is prohibitively burdensome for GGCAT.Our construction algorithm of Prokrustean graph utilizes an (extended) Burrows-Wheeler transform as input, is easily parallelizable, and operates inO(N) time whereNis the cumulative input sequence length. We provide theoretical justification that the size of a Prokrustean graph isO(N), and in practice, is significantly smaller thanN.All code and algorithms are publicly accessible at:https://github.com/KoslickiLab/prokrustean.

show abstract

Towards a Complete Perspective on Labeled Tree Indexing: New Size Bounds, Efficient Constructions, and Beyond

Inenaga

2021

Journal of Information Processing

View full text Add to dashboard Cite

A labeled tree (or a trie) is a natural generalization of a string which can also be seen as a compact representation of a set of strings. This paper considers the labeled tree indexing problem, and provides a number of new results on space bound analysis and on algorithms for efficient construction and pattern matching queries. Kosaraju [FOCS 1989] was the first to consider the labeled tree indexing problem and he proposed the suffix tree for a backward trie, where the strings in the trie are read in the leaf-to-root direction. In contrast to a backward trie, we call an ordinary trie as a forward trie. Despite a few follow-up works after Kosaraju's paper, indexing forward/backward tries is not well understood yet. In this paper, we show a full perspective on the sizes of indexing structures such as suffix trees, DAWGs, CDAWGs, suffix arrays, affix trees, affix arrays for forward and backward tries. Some of them take O(n) space in the size n of the input trie, while the others can occupy O(n 2 ) space in the worst case. In particular, we show that the size of the DAWG for a forward trie with n nodes is Ω(σn), where σ is the number of distinct characters in the trie. This becomes Ω(n 2 ) for an alphabet of size σ = Θ(n). Still, we show that there is a compact O(n)-space implicit representation of the DAWG for a forward trie, whose space requirement is independent of the alphabet size. This compact representation allows for simulating each DAWG edge traversal in O(log σ) time, and can be constructed in O(n) time and space over any integer alphabet of size O(n). In addition, this readily extends to the first indexing structure that permits bidirectional pattern searches over a trie within linear space in the input trie size. We also discuss the size of the DAWG built on a labeled DAG or on an acyclic DFA, and present a quadratic lower bound for its size.

show abstract

Smaller Fully-Functional Bidirectional BWT Indexes

Cited by 3 publications

References 51 publications

Linear-time computation of DAWGs, symmetric indexing structures, and MAWs for integer alphabets

Linear-time computation of DAWGs, symmetric indexing structures, and MAWs for integer alphabets

Prokrustean Graph: A substring index for rapid k-mer size analysis

Towards a Complete Perspective on Labeled Tree Indexing: New Size Bounds, Efficient Constructions, and Beyond

Contact Info

Product

Resources

About