Approximate String Matching Problem Research Articles

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 clear step towards extending (compressed) suffix tree functionalities to labeled graphs.

On the complexity of approximately matching a string to a directed graph

The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields. In this paper we present results on the complexity of the approximate matching problem, where edit operations are symbol substitutions and are allowed only to the graph labels or both to the graph labels and the query string. We show that deciding if there exists a path in a graph that represents a query string with edit operations to vertex labels is an NP-complete problem and it is fixed-parameter tractable when parameterized by the length of the input string. We show that the variants of approximate string matching we consider are not fixed-parameter tractable, when the parameter is (1) the length of the query string and (2) the number of edit operations. Moreover, we provide inapproximability results for these variants of the of approximate string matching problem.

SneakySnake: a fast and accurate universal genome pre-alignment filter for CPUs, GPUs and FPGAs.

We introduce SneakySnake, a highly parallel and highly accurate pre-alignment filter that remarkably reduces the need for computationally costly sequence alignment. The key idea of SneakySnake is to reduce the approximate string matching (ASM) problem to the single net routing (SNR) problem in VLSI chip layout. In the SNR problem, we are interested in finding the optimal path that connects two terminals with the least routing cost on a special grid layout that contains obstacles. The SneakySnake algorithm quickly solves the SNR problem and uses the found optimal path to decide whether or not performing sequence alignment is necessary. Reducing the ASM problem into SNR also makes SneakySnake efficient to implement on CPUs, GPUs and FPGAs. SneakySnake significantly improves the accuracy of pre-alignment filtering by up to four orders of magnitude compared to the state-of-the-art pre-alignment filters, Shouji, GateKeeper and SHD. For short sequences, SneakySnake accelerates Edlib (state-of-the-art implementation of Myers's bit-vector algorithm) and Parasail (state-of-the-art sequence aligner with a configurable scoring function), by up to 37.7× and 43.9× (>12× on average), respectively, with its CPU implementation, and by up to 413× and 689× (>400× on average), respectively, with FPGA and GPU acceleration. For long sequences, the CPU implementation of SneakySnake accelerates Parasail and KSW2 (sequence aligner of minimap2) by up to 979× (276.9× on average) and 91.7× (31.7× on average), respectively. As SneakySnake does not replace sequence alignment, users can still obtain all capabilities (e.g. configurable scoring functions) of the aligner of their choice, unlike existing acceleration efforts that sacrifice some aligner capabilities. https://github.com/CMU-SAFARI/SneakySnake. Supplementary data are available at Bioinformatics online.

Secure Approximate String Matching for Privacy-Preserving Record Linkage

Real-world applications of record linkage often require matching to be robust in spite of small variations in string fields. For example, two health care providers should be able to detect a patient in common, even if one record contains a typo or transcription error. In the privacy-preserving setting, however, the problem of approximate string matching has been cast as a trade-off between security and practicality, and the literature has mainly focused on Bloom filter encodings , an approach which can leak significant information about the underlying records. We present a novel public-key construction for secure two-party evaluation of threshold functions in restricted domains based on embeddings found in the message spaces of additively homomorphic encryption schemes. We use this to construct an efficient two-party protocol for privately computing the threshold Dice coefficient. Relative to the approach of Bloom filter encodings, our proposal offers formal security guarantees and greater matching accuracy. We implement the protocol and demonstrate the feasibility of this approach in linking medium-sized patient databases with tens of thousands of records.

GateKeeper: a new hardware architecture for accelerating pre-alignment in DNA short read mapping.

High throughput DNA sequencing (HTS) technologies generate an excessive number of small DNA segments -called short reads- that cause significant computational burden. To analyze the entire genome, each of the billions of short reads must be mapped to a reference genome based on the similarity between a read and 'candidate' locations in that reference genome. The similarity measurement, called alignment, formulated as an approximate string matching problem, is the computational bottleneck because: (i) it is implemented using quadratic-time dynamic programming algorithms and (ii) the majority of candidate locations in the reference genome do not align with a given read due to high dissimilarity. Calculating the alignment of such incorrect candidate locations consumes an overwhelming majority of a modern read mapper's execution time. Therefore, it is crucial to develop a fast and effective filter that can detect incorrect candidate locations and eliminate them before invoking computationally costly alignment algorithms. We propose GateKeeper, a new hardware accelerator that functions as a pre-alignment step that quickly filters out most incorrect candidate locations. GateKeeper is the first design to accelerate pre-alignment using Field-Programmable Gate Arrays (FPGAs), which can perform pre-alignment much faster than software. When implemented on a single FPGA chip, GateKeeper maintains high accuracy (on average >96%) while providing, on average, 90-fold and 130-fold speedup over the state-of-the-art software pre-alignment techniques, Adjacency Filter and Shifted Hamming Distance (SHD), respectively. The addition of GateKeeper as a pre-alignment step can reduce the verification time of the mrFAST mapper by a factor of 10. https://github.com/BilkentCompGen/GateKeeper. mohammedalser@bilkent.edu.tr or onur.mutlu@inf.ethz.ch or calkan@cs.bilkent.edu.tr. Supplementary data are available at Bioinformatics online.

Weighted approximate parameterized string matching

We consider the problem of finding a bijection to match a pattern in a text where both the pattern and the text are strings from distinct alphabets. The objective of weighted approximate parameterized string matching problem is to find approximate parameterized pattern of length m match under weighted Hamming distance in a text of length n. Our main result is an O(nm) time algorithm for this problem. We also investigate string comparison problem with k threshold under weighted Hamming distance and give a O(m+k) time solution. All the above time complexities assume constant size alphabets.

LibFLASM: a software library for fixed-length approximate string matching.

BackgroundApproximate string matching is the problem of finding all factors of a given text that are at a distance at most k from a given pattern. Fixed-length approximate string matching is the problem of finding all factors of a text of length n that are at a distance at most k from any factor of length ℓ of a pattern of length m. There exist bit-vector techniques to solve the fixed-length approximate string matching problem in time mathcal {O}(mlceil ell /w rceil n) and space mathcal {O}(mlceil ell /wrceil) under the edit and Hamming distance models, where w is the size of the computer word; as such these techniques are independent of the distance threshold k or the alphabet size. Fixed-length approximate string matching is a generalisation of approximate string matching and, hence, has numerous direct applications in computational molecular biology and elsewhere.ResultsWe present and make available libFLASM, a free open-source C++ software library for solving fixed-length approximate string matching under both the edit and the Hamming distance models. Moreover we describe how fixed-length approximate string matching is applied to solve real problems by incorporating libFLASM into established applications for multiple circular sequence alignment as well as single and structured motif extraction. Specifically, we describe how it can be used to improve the accuracy of multiple circular sequence alignment in terms of the inferred likelihood-based phylogenies; and we also describe how it is used to efficiently find motifs in molecular sequences representing regulatory or functional regions. The comparison of the performance of the library to other algorithms show how it is competitive, especially with increasing distance thresholds.ConclusionsFixed-length approximate string matching is a generalisation of the classic approximate string matching problem. We present libFLASM, a free open-source C++ software library for solving fixed-length approximate string matching. The extensive experimental results presented here suggest that other applications could benefit from using libFLASM, and thus further maintenance and development of libFLASM is desirable.

Read mapping

Abstract The Read Mapping problem asks for the exact origin of a nucleotide sequence in a reference genome. It translates to a conceptually simple approximate string matching problem. The practical difficulty, however, arises from the typical size of the data sets produced by modern high throughput sequencing technologies, from the biological processes involved in derivation of the query molecule from its genomic source, and from the technical processes of the sequencing technology itself.

MoTeX-II: structured MoTif eXtraction from large-scale datasets.

BackgroundIdentifying repeated factors that occur in a string of letters or common factors that occur in a set of strings represents an important task in computer science and biology. Such patterns are called motifs, and the process of identifying them is called motif extraction. In biology, motif extraction constitutes a fundamental step in understanding regulation of gene expression. State-of-the-art tools for motif extraction have their own constraints. Most of these tools are only designed for single motif extraction; structured motifs additionally allow for distance intervals between their single motif components. Moreover, motif extraction from large-scale datasets—for instance, large-scale ChIP-Seq datasets—cannot be performed by current tools. Other constraints include high time and/or space complexity for identifying long motifs with higher error thresholds.ResultsIn this article, we introduce MoTeX-II, a word-based high-performance computing tool for structured MoTif eXtraction from large-scale datasets. Similar to its predecessor for single motif extraction, it uses state-of-the-art algorithms for solving the fixed-length approximate string matching problem. It produces similar and partially identical results to state-of-the-art tools for structured motif extraction with respect to accuracy as quantified by statistical significance measures. Moreover, we show that it matches or outperforms these tools in terms of runtime efficiency by merging single motif occurrences efficiently. MoTeX-II comes in three flavors: a standard CPU version; an OpenMP-based version; and an MPI-based version. For instance, the MPI-based version of MoTeX-II requires only a couple of hours to process all human genes for structured motif extraction on 1056 processors, while current sequential tools require more than a week for this task. Finally, we show that MoTeX-II is successful in extracting known composite transcription factor binding sites from real datasets.ConclusionsUse of MoTeX-II in biological frameworks may enable deriving reliable and important information since real full-length datasets can now be processed with almost any set of input parameters for both single and structured motif extraction in a reasonable amount of time. The open-source code of MoTeX-II is freely available at http://www.inf.kcl.ac.uk/research/projects/motex/.

Approximate Chinese String Matching Techniques Based on Pinyin Input Method

String matching is one of the most typical problems in computer science. Previous studies mainly focused on accurate string matching problem. However, with the rapid development of the computer and Internet as well as the continuously rising of new issues, people find that it has very important theoretical value and practical meaning to research and design efficient approximate string matching algorithms. Approximate string matching is also called string matching that allows errors, which mainly aims to find the pattern string in the text and database and allows k differences between the pattern string and its occurring forms in the text. For the problem of approximate string matching, though a number of algorithms have been proposed, there are fewer studies which focus on large size of alphabet . Most of experts are interested in small or middle size of alphabet . For large size of , especially for Chinese characters and Asian phonetics, there are fewer efficient algorithms. For the above reasons, this paper focuses on the approximate Chinese strings matching problem based on the pinyin input method.

A graph-theoretic model to solve the approximate string matching problem allowing for translocations

In this paper, we study the approximate string matching problem under a string distance whose edit operations are translocations of equal length factors. We extend a graph-theoretic approach proposed by Rahman and Illiopoulos (2008) to model our problem. In the sequel, we devise efficient algorithms based on this model to solve a number of variants of the string matching problem with translocations.

Text searching allowing for inversions and translocations of factors

The approximate string matching problem consists in finding all locations at which a pattern p of length m matches a substring of a text t of length n, after a finite number of given edit operations.In this paper, we investigate such a problem when the edit operations are translocations of adjacent factors of equal length and inversions of factors. In particular, we first present an O(nmmax(α,β))-time and O(m2)-space algorithm, where α and β are respectively the maximum lengths of the factors which can be involved in any translocation and inversion, and show that under the assumptions of equiprobability and independence of characters our algorithm has a O(nlogσm) average time complexity, for an alphabet of size σ. We also present a very fast variant of a recently proposed algorithm for the same problem, based on an efficient filtering method, which has a O(n)-time complexity in the average case, though in the worst case it retains the same O(nmmax(α,β))-time complexity.

A new filtration method and a hybrid strategy for approximate string matching

In this paper, we propose a new filtration algorithm, as well as a hybrid filtration strategy, to efficiently solve the approximate string matching problem (also called the k-difference problem), which aims to find all the positions i’s in a given text such that there exists a substring of the text ending at position i whose edit distance from a given pattern is less than or equal to a given error bound k. Our experimental results on simulated datasets of DNA sequences show that when compared with other filtration algorithms, our filtration algorithm has better performance on the efficiency to filter out those positions of the text at which the pattern does not occur approximately. Moreover, our hybrid filtration strategy further improves the effectiveness of our filtration algorithm.

Efficient string-matching allowing for non-overlapping inversions

Inversions are a class of chromosomal mutations, widely regarded as one of the major mechanisms for reorganizing the genome.In this paper we present a new algorithm for the approximate string matching problem allowing for non-overlapping inversions which runs in O(nm) worst-case time and O(m2) space, for a character sequence of size n and pattern of size m. This improves upon a previous O(nm2)-time algorithm.In addition we present a variant of our algorithm with the same complexity in the worst case, but with a O(n) time complexity in the average case.

Pattern matching through Chaos Game Representation: bridging numerical and discrete data structures for biological sequence analysis

BackgroundChaos Game Representation (CGR) is an iterated function that bijectively maps discrete sequences into a continuous domain. As a result, discrete sequences can be object of statistical and topological analyses otherwise reserved to numerical systems. Characteristically, CGR coordinates of substrings sharing an L-long suffix will be located within 2-L distance of each other. In the two decades since its original proposal, CGR has been generalized beyond its original focus on genomic sequences and has been successfully applied to a wide range of problems in bioinformatics. This report explores the possibility that it can be further extended to approach algorithms that rely on discrete, graph-based representations.ResultsThe exploratory analysis described here consisted of selecting foundational string problems and refactoring them using CGR-based algorithms. We found that CGR can take the role of suffix trees and emulate sophisticated string algorithms, efficiently solving exact and approximate string matching problems such as finding all palindromes and tandem repeats, and matching with mismatches. The common feature of these problems is that they use longest common extension (LCE) queries as subtasks of their procedures, which we show to have a constant time solution with CGR. Additionally, we show that CGR can be used as a rolling hash function within the Rabin-Karp algorithm.ConclusionsThe analysis of biological sequences relies on algorithmic foundations facing mounting challenges, both logistic (performance) and analytical (lack of unifying mathematical framework). CGR is found to provide the latter and to promise the former: graph-based data structures for sequence analysis operations are entailed by numerical-based data structures produced by CGR maps, providing a unifying analytical framework for a diversity of pattern matching problems.

On-line approximate string matching with bounded errors

We introduce a new dimension to the widely studied on-line approximate string matching problem, by introducing an error threshold parameter ϵ so that the algorithm is allowed to miss occurrences with probability ϵ. This is particularly appropriate for this problem, as approximate searching is used to model many cases where exact answers are not mandatory. We show that the relaxed version of the problem allows us breaking the average-case optimal lower bound of the classical problem, achieving average case O(nlogσm/m) time with any ϵ=poly(k/m), where n is the text size, m the pattern length, k the number of differences for edit distance, and σ the alphabet size. Our experimental results show the practicality of this novel and promising research direction. Finally, we extend the proposed approach to the multiple approximate string matching setting, where the approximate occurrence of r patterns are simultaneously sought. Again, we can break the average-case optimal lower bound of the classical problem, achieving average case O(nlogσ(rm)/m) time with any ϵ=poly(k/m).

Faster Approximate String Matching for Short Patterns

We study the classical approximate string matching problem, that is, given strings P and Q and an error threshold k, find all ending positions of substrings of Q whose edit distance to P is at most k. Let P and Q have lengths m and n, respectively. On a standard unit-cost word RAM with word size w≥log n we present an algorithm using time $$O\biggl(nk \cdot \min\biggl(\frac{\log^2 m}{\log n},\frac{\log^2 m\log w}{w}\biggr) + n\biggr)$$ When P is short, namely, $m = 2^{o(\sqrt{\log n}\,)}$ or $m =2^{o(\sqrt{w/\log w}\,)}$ this improves the previously best known time bounds for the problem. The result is achieved using a novel implementation of the Landau-Vishkin algorithm based on tabulation and word-level parallelism.

Efficient computations of [formula omitted] and [formula omitted] rearrangement distances

Recently, a new pattern matching paradigm was proposed, pattern matching with address errors. In this paradigm approximate string matching problems are studied, where the content is unaltered and only the locations of the different entries may change. Specifically, a broad class of problems was defined—the class of rearrangement errors. In this type of error the pattern is transformed through a sequence of rearrangement operations, each with an associated cost. The natural ℓ 1 and ℓ 2 rearrangement systems were considered. The best algorithm presented for general patterns, that may have repeating symbols, is O ( n m ) . In this paper, we show that the problem can be approximated in linear time for general patterns! Another natural rearrangement system is considered in this paper—the ℓ ∞ rearrangement distance. For this new rearrangement system efficient exact solutions for different variants of the problem are provided, as well as a faster approximation.

Improved algorithms for approximate string matching (extended abstract)

BackgroundThe problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants of the problem, including comparison of two strings, approximate pattern identification in a string or calculation of the longest common subsequence that two strings share.ResultsWe designed an output sensitive algorithm solving the edit distance problem between two strings of lengths n and m respectively in time O((s - |n - m|)·min(m, n, s) + m + n) and linear space, where s is the edit distance between the two strings. This worst-case time bound sets the quadratic factor of the algorithm independent of the longest string length and improves existing theoretical bounds for this problem. The implementation of our algorithm also excels in practice, especially in cases where the two strings compared differ significantly in length.ConclusionWe have provided the design, analysis and implementation of a new algorithm for calculating the edit distance of two strings with both theoretical and practical implications. Source code of our algorithm is available online.

Parallel Algorithms for String Matching Problem on Single and Two Dimensional Reconfigurable Pipelined Bus Systems

We considered string matching on LARPBS and 2D LARPBS. This has applications such as string databases, cellular automata and computational biology. The main use of this method is to reduce the time spent on comparisons in string matching by using LARPBS. We investigated exact string matching and approximate string matching problems. For these two sub problems, we obtained O (n) bus cycles algorithm and constant bus cycles algorithm. These algorithms have some disadvantages: Reconnecting the sub buses and shuffling the contents .These problems can be solved by 2D LARPBS.