Inducing the LCP-Array

Computing the BWT and LCP array of a Set of Strings in External Memory

Indexing very large collections of strings, such as those produced by the widespread next generation sequencing technologies, heavily relies on multistring generalization of the Burrows-Wheeler Transform (BWT): large requirements of in-memory approaches have stimulated recent developments on external memory algorithms. The related problem of computing the Longest Common Prefix (LCP) array of a set of strings is instrumental to compute the suffix-prefix overlaps among strings, which is an essential step for many genome assembly algorithms. In a previous paper, we presented an in-memory divide-a…

Wee LCP

We prove that longest common prefix (LCP) information can be stored in much less space than previously known. More precisely, we show that in the presence of the text and the suffix array, o(n) additional bits are sufficient to answer LCP-queries asymptotically in the same time that is needed to retrieve an entry from the suffix array. This yields the smallest compressed suffix tree with sub-logarithmic navigation time.

计算有标号图的 LCP 数组

Computing the LCP Array of a Labeled Graph

本文提出了首个基于动态范围刺穿的高效算法，可在 $O(n\log σ)$ 时间和 $O(n\logσ)$ 位空间内构建有向有标号图的 LCP 数组。

A New Lightweight Algorithm to compute the BWT and the LCP array of a Set of Strings

Indexing of very large collections of strings such as those produced by the widespread sequencing technologies, heavily relies on multi-string generalizations of the Burrows-Wheeler Transform (BWT), and for this problem various in-memory algorithms have been proposed. The rapid growing of data that are processed routinely, such as in bioinformatics, requires a large amount of main memory, and this fact has motivated the development of algorithms, to compute the BWT, that work almost entirely in external memory. On the other hand, the related problem of computing the Longest Common Prefix (LCP)…

Low Space External Memory Construction of the Succinct Permuted Longest Common Prefix Array

The longest common prefix (LCP) array is a versatile auxiliary data structure in indexed string matching. It can be used to speed up searching using the suffix array (SA) and provides an implicit representation of the topology of an underlying suffix tree. The LCP array of a string of length $n$ can be represented as an array of length $n$ words, or, in the presence of the SA, as a bit vector of $2n$ bits plus asymptotically negligible support data structures. External memory construction algorithms for the LCP array have been proposed, but those proposed so far have a space requirement of $O(…

Wheeler DFA的LCP数组的时空权衡

Space-time Trade-offs for the LCP Array of Wheeler DFAs

针对Wheeler DFA的LCP数组存储占用高的问题，提出仅需线性比特、对数时间访问的采样技术，实现匹配统计计算的时空权衡，并改进了变阶德布鲁因图遍历的时间界。

Space-Efficient Computation of the LCP Array from the Burrows-Wheeler Transform

We show that the Longest Common Prefix Array of a text collection of total size n on alphabet [1, σ] can be computed from the Burrows-Wheeler transformed collection in O(n log σ) time using o(n log σ) bits of working space on top of the input and output. Our result improves (on small alphabets) and generalizes (to string collections) the previous solution from Beller et al., which required O(n) bits of extra working space. We also show how to merge the BWTs of two collections of total size n within the same time and space bounds. The procedure at the core of our algorithms can be used to enume…

Dismantling DivSufSort

We give the first concise description of the fastest known suffix sorting algorithm in main memory, the DivSufSort by Yuta Mori. We then present an extension that also computes the LCP-array, which is competitive with the fastest known LCP-array construction algorithm.

External memory BWT and LCP computation for sequence collections with applications

We propose an external memory algorithm for the computation of the BWT and LCP array for a collection of sequences. Our algorithm takes the amount of available memory as an input parameter, and tries to make the best use of it by splitting the input collection into subcollections sufficiently small that it can compute their BWT in RAM using an optimal linear time algorithm. Next, it merges the partial BWTs in external memory and in the process it also computes the LCP values. We prove that our algorithm performs O(n AveLcp) sequential I/Os, where n is the total length of the collection, and Av…

用于简洁 k-谱的最长公共前缀数组

Longest Common Prefix Arrays for Succinct k-Spectra

本文研究从 k-谱的 SBWT 表示构造 LCP 数组，提出 O(nk) 直接算法、最优 O(n) 算法及缓存友好的次优算法，以支持伪比对加速和变阶 de Bruijn 图模拟。

稀疏后缀数组与LCP数组：简单、直接、紧凑且快速

Sparse Suffix and LCP Array: Simple, Direct, Small, and Fast

本文提出两种构造稀疏后缀数组与LCP数组的新算法，兼具简单、直接、紧凑和快速特性，最坏时间O(n log b)，空间仅8b+o(b)机器字，并通过实验验证其简单性与高效性。

Lightweight LCP Construction for Very Large Collections of Strings

The longest common prefix array is a very advantageous data structure that, combined with the suffix array and the Burrows-Wheeler transform, allows to efficiently compute some combinatorial properties of a string useful in several applications, especially in biological contexts. Nowadays, the input data for many problems are big collections of strings, for instance the data coming from "next-generation" DNA sequencing (NGS) technologies. In this paper we present the first lightweight algorithm (called extLCP) for the simultaneous computation of the longest common prefix array and the Burrows-…

Computing matching statistics on Wheeler DFAs

Matching statistics were introduced to solve the approximate string matching problem, which is a recurrent subroutine in bioinformatics applications. In 2010, Ohlebusch et al. [SPIRE 2010] proposed a time and space efficient algorithm for computing matching statistics which relies on some components of a compressed suffix tree - notably, the longest common prefix (LCP) array. In this paper, we show how their algorithm can be generalized from strings to Wheeler deterministic finite automata. Most importantly, we introduce a notion of LCP array for Wheeler automata, thus establishing a first cle…

From H&M to Gap for Lightweight BWT Merging

Recently, Holt and McMillan [Bionformatics 2014, ACM-BCB 2014] have proposed a simple and elegant algorithm to merge the Burrows-Wheeler transforms of a family of strings. In this paper we show that the H&M algorithm can be improved so that, in addition to merging the BWTs, it can also merge the Longest Common Prefix (LCP) arrays. The new algorithm, called Gap because of how it operates, has the same asymptotic cost as the H&M algorithm and requires additional space only for storing the LCP values.

In-Place Sparse Suffix Sorting

Suffix arrays encode the lexicographical order of all suffixes of a text and are often combined with the Longest Common Prefix array (LCP) to simulate navigational queries on the suffix tree in reduced space. In space-critical applications such as sparse and compressed text indexing, only information regarding the lexicographical order of a size-$b$ subset of all $n$ text suffixes is often needed. Such information can be stored space-efficiently (in $b$ words) in the sparse suffix array (SSA). The SSA and its relative sparse LCP array (SLCP) can be used as a space-efficient substitute of the s…

Inducing the Lyndon Array

In this paper we propose a variant of the induced suffix sorting algorithm by Nong (TOIS, 2013) that computes simultaneously the Lyndon array and the suffix array of a text in $O(n)$ time using $σ+ O(1)$ words of working space, where $n$ is the length of the text and $σ$ is the alphabet size. Our result improves the previous best space requirement for linear time computation of the Lyndon array. In fact, all the known linear algorithms for Lyndon array computation use suffix sorting as a preprocessing step and use $O(n)$ words of working space in addition to the Lyndon array and suffix array. …

Optimal Substring-Equality Queries with Applications to Sparse Text Indexing

We consider the problem of encoding a string of length $n$ from an integer alphabet of size $σ$ so that access and substring equality queries (that is, determining the equality of any two substrings) can be answered efficiently. Any uniquely-decodable encoding supporting access must take $n\logσ+ Θ(\log (n\logσ))$ bits. We describe a new data structure matching this lower bound when $σ\leq n^{O(1)}$ while supporting both queries in optimal $O(1)$ time. Furthermore, we show that the string can be overwritten in-place with this structure. The redundancy of $Θ(\log n)$ bits and the constant query…

Grammar Compression By Induced Suffix Sorting

A grammar compression algorithm, called GCIS, is introduced in this work. GCIS is based on the induced suffix sorting algorithm SAIS, presented by Nong et al. in 2009. The proposed solution builds on the factorization performed by SAIS during suffix sorting. A context-free grammar is used to replace factors by non-terminals. The algorithm is then recursively applied on the shorter sequence of non-terminals. The resulting grammar is encoded by exploiting some redundancies, such as common prefixes between right-hands of rules, sorted according to SAIS. GCIS excels for its low space and time requ…

最优时间移动结构构造

Optimal-Time Move Structure Construction

本文提出一种最优时间与空间的移动结构构造算法，用于高效表示和导航排列，尤其在r远小于n时能显著压缩空间。