Bidirectional search in a string with wavelet trees and bidirectional matching statistics

Schnattinger, Thomas; Ohlebusch, Enno; Gog, Simon

doi:10.1016/j.ic.2011.03.007

Cited by 33 publications

(57 citation statements)

References 10 publications

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“…An insertion or a deletion of some document T u is supported in O(|T u | log ε n) and O(|T u |(log ε n + s)) deterministic time respectively. We believe that our technique can also improve upon some of the recently presented results on bidirectional FM-indices [42,5] and other scenarios where compressed suffix trees are used [6].…”

Section: Discussionmentioning

confidence: 57%

Space-Efficient Construction of Compressed Indexes in Deterministic Linear Time

Munro

Navarro

Nekrich

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We show that the compressed suffix array and the compressed suffix tree of a string T can be built in O(n) deterministic time using O(n log σ) bits of space, where n is the string length and σ is the alphabet size. Previously described deterministic algorithms either run in time that depends on the alphabet size or need ω(n log σ) bits of working space. Our result has immediate applications to other problems, such as yielding the first deterministic linear-time LZ77 and LZ78 parsing algorithms that use O(n log σ) bits.

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Section: Discussionmentioning

confidence: 57%

Space-Efficient Construction of Compressed Indexes in Deterministic Linear Time

Munro

Navarro

Nekrich

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…The BWT index can be made bidirectional, in the sense that it can be adapted to support both left and right extension by a single character [65,66]. In addition to having a number of applications in high-throughput sequencing (see e.g.…”

Section: Building the Bidirectional Bwt Indexmentioning

confidence: 99%

Linear-time String Indexing and Analysis in Small Space

Belazzougui

Cunial

Kärkkäinen

et al. 2020

ACM Trans. Algorithms

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The field of succinct data structures has flourished over the last 16 years. Starting from the compressed suffix array by Grossi and Vitter (STOC 2000) and the FM-index by Ferragina and Manzini (FOCS 2000), a number of generalizations and applications of string indexes based on the Burrows-Wheeler transform (BWT) have been developed, all taking an amount of space that is close to the input size in bits. In many large-scale applications, the construction of the index and its usage need to be considered as one unit of computation. For example, one can compare two genomes by building a common index for their concatenation, and by detecting common substructures by querying the index. Efficient string indexing and analysis in small space lies also at the core of a number of primitives in the data-intensive field of high-throughput DNA sequencing.We report the following advances in string indexing and analysis. We show that the BWT of a string T ∈ {1, . . . , σ} n can be built in deterministic O(n) time using just O(n log σ) bits of space, where σ ≤ n. Deterministic linear time is achieved by exploiting a new partial rank data structure that supports queries in constant time, and that might have independent interest. Within the same time and space budget, we can build an index based on the BWT that allows one to enumerate all the internal nodes of the suffix tree of T . Many fundamental string analysis problems, such as maximal repeats, maximal unique matches, and string kernels, can be mapped to such enumeration, and can thus be solved in deterministic O(n) time and in O(n log σ) bits of space from the input string, by tailoring the enumeration algorithm to some problem-specific computations.We also show how to build many of the existing indexes based on the BWT, such as the compressed suffix array, the compressed suffix tree, and the bidirectional BWT index, in randomized O(n) time and in O(n log σ) bits of space. The previously fastest construction algorithms for BWT, compressed suffix array and compressed suffix tree, which used O(n log σ) bits of space, took O(n log log σ) time for the first two structures, and O(n log ǫ n) time for the third, where ǫ is any positive constant smaller than one. Contrary to the state of the art, our bidirectional BWT index supports every operation in constant time per element in its output.

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“…For large alphabets, it is not practical to maintain for each character a bit vector with rank support. In 2003 Grossi et al [8] proposed the use of a more space efficient data structure for the FM index, called the (binary) wavelet tree (WT) that was later used by Schnattinger [18] for an implementation of bidirectional FM indices. It is a binary tree of height O(log σ) with a bit vector of length n with rank support at each level.…”

Section: Recent Improvements On the Fm And 2fm Indexmentioning

confidence: 99%

“…In its original form it allows to search exactly for a pattern in one direction by matching the characters of the pattern with characters in the BWT [3] (i.e., extending a suffix of the pattern character by character to the left). It was later extended to the 2FM index by Lam et al [10] and Schnattinger et al [18]. The 2FM index allows to search in both directions, that means we can extend an infix of a pattern arbitrarily to the left or to the right.…”

Section: Introductionmentioning

confidence: 99%

EPR-Dictionaries: A Practical and Fast Data Structure for Constant Time Searches in Unidirectional and Bidirectional FM Indices

Pockrandt¹,

Ehrhardt

Reinert

2017

Lecture Notes in Computer Science

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The unidirectional FM index was introduced by Ferragina and Manzini in 2000 and allows to search a pattern in the index in one direction. The bidirectional FM index (2FM) was introduced by Lam et al. in 2009. It allows to search for a pattern by extending an infix of the pattern arbitrarily to the left or right. The method of Lam et al. can conduct one step in time O(σ) while needing space O(σ · n) using constant time rank queries on bit vectors. Schnattinger and colleagues improved this time to O(log σ) while usingO(log σ · n) bits of space for both, the FM and 2FM index. This is achieved by the use of binary wavelet trees. In this paper we introduce a new, practical method for conducting an exact search in a uni-and bidirectional FM index in O(1) time per step while using O(log σ · n) + o(log σ · σ · n) bits of space. This is done by replacing the binary wavelet tree by a new data structure, the Enhanced Prefixsum Rank dictionary (EPR-dictionary). We implemented this method in the SeqAn C++ library and experimentally validated our theoretical results. In addition we compared our implementation with other freely available implementations of bidirectional indices and show that we are between ≈ 2.6 − 4.8 times faster. This will have a large impact for many bioinformatics applications that rely on practical implementations of (2)FM indices e.g. for read mapping. To our knowledge this is the first implementation of a constant time method for a search step in 2FM indices.

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Bidirectional search in a string with wavelet trees and bidirectional matching statistics

Cited by 33 publications

References 10 publications

Space-Efficient Construction of Compressed Indexes in Deterministic Linear Time

Space-Efficient Construction of Compressed Indexes in Deterministic Linear Time

Linear-time String Indexing and Analysis in Small Space

EPR-Dictionaries: A Practical and Fast Data Structure for Constant Time Searches in Unidirectional and Bidirectional FM Indices

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