String Matching Problem Research Articles

Elastic-Degenerate String Matching with 1 Error or Mismatch

An elastic-degenerate (ED) string is a sequence of n finite sets of strings of total length N, introduced to represent a set of related DNA sequences, also known as a pangenome. The ED string matching (EDSM) problem consists in reporting all occurrences of a pattern of length m in an ED text. The EDSM problem has recently received some attention by the combinatorial pattern matching community, culminating in an O~(nmω-1)+O(N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {\ ilde{O}}(nm^{\\omega -1})+\\mathcal {O}(N)$$\\end{document}-time algorithm [Bernardini et al., SIAM J. Comput. 2022], where ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} denotes the matrix multiplication exponent and the O~(·)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {\ ilde{O}}(\\cdot )$$\\end{document} notation suppresses polylog factors. In the k-EDSM problem, the approximate version of EDSM, we are asked to report all pattern occurrences with at most k errors. k-EDSM can be solved in O(k2mG+kN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(k^2mG+kN)$$\\end{document} time, under edit distance, or O(kmG+kN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(kmG+kN)$$\\end{document} time, under Hamming distance, where G denotes the total number of strings in the ED text [Bernardini et al., Theor. Comput. Sci. 2020]. Unfortunately, G is only bounded by N, and so even for k=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=1$$\\end{document}, the existing algorithms run in Ω(mN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varOmega (mN)$$\\end{document} time in the worst case. In this paper we make progress in this direction. We show that 1-EDSM can be solved in O((nm2+N)logm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}((nm^2 + N)\\log m)$$\\end{document} or O(nm3+N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(nm^3 + N)$$\\end{document} time under edit distance. For the decision version of the problem, we present a faster O(nm2logm+Nloglogm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(nm^2\\sqrt{\\log m} + N\\log \\log m)$$\\end{document}-time algorithm. We also show that 1-EDSM can be solved in O(nm2+Nlogm)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {O}(nm^2 + N\\log m)$$\\end{document} time under Hamming distance. Our algorithms for edit distance rely on non-trivial reductions from 1-EDSM to special instances of classic computational geometry problems (2d rectangle stabbing or 2d range emptiness), which we show how to solve efficiently. In order to obtain an even faster algorithm for Hamming distance, we rely on employing and adapting the k-errata trees for indexing with errors [Cole et al., STOC 2004]. This is an extended version of a paper presented at LATIN 2022.

Graphs cannot be indexed in polynomial time for sub-quadratic time string matching, unless SETH fails

The string matching problem on a node-labeled graph G=(V,E) asks whether a given pattern string P equals the concatenation of node labels of some path in G. This is a basic primitive in various problems in bioinformatics, graph databases, or networks, and it was recently proven that solving it in time O(|E|1−ϵ|P|) or O(|E||P|1−ϵ) is hard under OVH, the Orthogonal Vectors Hypothesis, and thus under SETH, the Strong Exponential Time Hypothesis (Equi et al., 2019 [11]). We consider its indexed version, where the graph is indexed to support string queries. We show that, under OVH, no polynomial-time index of the graph performed in time O(|E|α) can support querying P in time O(|P|+|E|δ|P|β), with either δ<1 or β<1.We present our techniques as a general framework, introducing the notion of linear independent-components (lic) reduction, from which we derive our result. This allows us to also translate the quadratic conditional lower bound of Backurs and Indyk (2015) [48] for the problem of matching a query string inside a text, under edit distance, into an analogous tight quadratic lower bound for its indexed version. This improves the recent result of Cohen-Addad, Feuilloley and Starikovskaya (2019) [49], with a slightly different boundary condition. We also apply our technique to obtain the first quadratic indexing lower bounds for Fréchet distance and rooted unlabeled subtree-isomorphism queries.

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.

PARALLEL PROCESSING OUTCOMES OF E-ABDULRAZZAQ ALGORITHM USING MULTI-CORE TECHNIQUE

The string matching problem is considered one of the substantial problems in the fields of computer science like speech and pattern recognition, signal and image processing, and artificial intelligence (AI). The increase in the speedup of performance is considered an important factor in meeting the growth rate of databases, Subsequently, one of the determinations to address this issue is the parallelization for exact string matching algorithms. In this study, the E-Abdulrazzaq string matching algorithm is chosen to be executed with the multi-core environment utilizing the OpenMP paradigm which can be utilized to decrease the execution time and increase the speedup of the algorithm. The parallelization algorithm got positive results within the parallel execution time, and excellent speeding-up capabilities, in comparison to the successive result. The Protein database showed optimal results in parallel execution time, and when utilizing short and long pattern lengths. The DNA database showed optimal speedup execution when utilizing short and long pattern lengths, while no specific database obtained the worst results.

Compact suffix automata representations for searching long patterns

Automata based algorithms have always dominated the history of string matching, thanks to their intrinsic nature of recognizers. Among them, those based on the suffix automaton deserve a special mention, because its use has always led to elegant and very efficient solutions in practice. In this paper, we present two novel string matching algorithms based on the suffix automaton which are particularly suitable for very long strings. The first algorithm simulates the suffix automaton through the well known bit-parallelism approach, while the second makes use of an alternative non-standard simulation. We mainly focus on the second solution, which turns out to be more flexible in practice, and present some extensions of it. Experimental results suggest that both our solutions are very efficient in practical cases scaling much better when the length of the pattern increases. Moreover, our second approach is also competitive with the most effective solutions available for the exact string matching problem.

A weak approach to suffix automata simulation for exact and approximate string matching

String matching is one of the most extensively studied problems in computer science, mainly due to its direct applications to such diverse areas as text, image and signal processing, speech analysis and recognition, information retrieval, data compression, computational biology and chemistry. In the last few decades a myriad of alternative solutions have been proposed, based on very different techniques. However, automata have always played a very important role in the design of efficient string matching algorithms. In this paper we present the Range Automaton, a weak yet efficient variant of the non-deterministic suffix automaton of a string whose configuration can be encoded in a very simple form and which is particularly suitable to be used for solving a multitude of text-searching problems. We will firstly develop our approach in the case of exact string matching and present an efficient algorithm, named Backward Range Automaton Matcher, which turns out to be very fast in many practical cases. Later, we will show how the Range Automaton can be adapted in an effective way also to non-standard string matching problems such as swap matching and multiple string matching. Experimental results suggest that our approach is flexible and effective for all three search problems addressed, especially in the case of long patterns.

Classification and Recognition of Bilingual Text Using Graph Edit Distance Based Degree of Similarity

Objectives: Graph Edit distance-based classification and recognition method is introduced in this study for bilingual characters. Specifically, this method aims to classify characters first and then recognize them in the 2nd level. Methods: This study combines both exact graph matching and inexact graph matching techniques to achieve better Recognition. The exact graph matching technique classifies characters by considering the number of vertices and edges as features to classify. Inexact graph matching uses an algorithmic model to measure the degree of similarity in the length of edit operations. Findings: The proposed model can compute, if not optimal, sequences all the time, at least near-optimal edit sequence. The proposed model is based on dynamic programming. Edit distance is estimated by comparing preorder sequences of the respective binary trees. Finally, this model uses the loss function to recognize text accurately. To bring out the practicality of the proposed model, we present a case study on the classification of English alphabets and Kannada conjunct consonants. Novelty: (i) A hybrid approach for converting a large class classification problem into a small classification problem that takes advantage of both exact and inexact graph matching techniques. (ii) An algorithmic model is designed to represent each character as a unique string. (iii) Uses dynamic programming in the right places to get the optimal tree, and (iv) to convert the graph matching problem to a string matching problem reduces the time complexity of the problem. Keywords: Bilingual text; Character Recognition; Degree of Similarity; Graph Edit Distance; Graph Matching

Identification of all-against-all protein–protein interactions based on deep hash learning

BackgroundProtein–protein interaction (PPI) is vital for life processes, disease treatment, and drug discovery. The computational prediction of PPI is relatively inexpensive and efficient when compared to traditional wet-lab experiments. Given a new protein, one may wish to find whether the protein has any PPI relationship with other existing proteins. Current computational PPI prediction methods usually compare the new protein to existing proteins one by one in a pairwise manner. This is time consuming.ResultsIn this work, we propose a more efficient model, called deep hash learning protein-and-protein interaction (DHL-PPI), to predict all-against-all PPI relationships in a database of proteins. First, DHL-PPI encodes a protein sequence into a binary hash code based on deep features extracted from the protein sequences using deep learning techniques. This encoding scheme enables us to turn the PPI discrimination problem into a much simpler searching problem. The binary hash code for a protein sequence can be regarded as a number. Thus, in the pre-screening stage of DHL-PPI, the string matching problem of comparing a protein sequence against a database with M proteins can be transformed into a much more simpler problem: to find a number inside a sorted array of length M. This pre-screening process narrows down the search to a much smaller set of candidate proteins for further confirmation. As a final step, DHL-PPI uses the Hamming distance to verify the final PPI relationship.ConclusionsThe experimental results confirmed that DHL-PPI is feasible and effective. Using a dataset with strictly negative PPI examples of four species, DHL-PPI is shown to be superior or competitive when compared to the other state-of-the-art methods in terms of precision, recall or F1 score. Furthermore, in the prediction stage, the proposed DHL-PPI reduced the time complexity from O(M^2) to O(Mlog M) for performing an all-against-all PPI prediction for a database with M proteins. With the proposed approach, a protein database can be preprocessed and stored for later search using the proposed encoding scheme. This can provide a more efficient way to cope with the rapidly increasing volume of protein datasets.

Elastic-Degenerate String Matching via Fast Matrix Multiplication

An elastic-degenerate (ED) string is a sequence of $n$ sets of strings of total length $N$, which was recently proposed to model a set of similar sequences. The ED string matching (EDSM) problem is to find all occurrences of a pattern of length $m$ in an ED text. An $O(nm^{1.5}\sqrt{\log m}+N)$-time algorithm for EDSM is known [Aoyama et al., CPM 2018]. The standard assumption in the prior work on this question is that $N$ is substantially larger than both $n$ and $m$, and thus we would like to have a linear dependency on the former. Under this assumption, the natural open problem is whether we can decrease the 1.5 exponent in the time complexity, similarly as in the related (but, to the best of our knowledge, not equivalent) word break problem [Backurs and Indyk, FOCS 2016]. Our starting point is a conditional lower bound for EDSM. We use the popular combinatorial Boolean Matrix Multiplication (BMM) conjecture stating that there is no truly subcubic combinatorial algorithm for BMM [Abboud and Williams, FOCS 2014]. By designing an appropriate reduction we show that a combinatorial algorithm solving the EDSM problem in $O(nm^{1.5-e}+N)$ time, for any $e>0$, refutes this conjecture. Our reduction should be understood as an indication that decreasing the exponent requires fast matrix multiplication. String periodicity and fast Fourier transform are two standard tools in string algorithms. Our main technical contribution is that we successfully combine these tools with fast matrix multiplication to design a non-combinatorial $\tilde{O}(nm^{\omega-1}+N)$-time algorithm for EDSM, where $\omega$ denotes the matrix multiplication exponent. To the best of our knowledge, we are the first to combine these tools. In particular, using the fact that $\omega<2.373$ [Le Gall, ISSAC 2014; Williams, STOC 2012], we obtain an $O(nm^{1.373}+N)$-time algorithm for EDSM.

On the average-case complexity of pattern matching with wildcards

Pattern matching with wildcards is a string matching problem with the goal of finding all factors of a text t of length n that match a pattern x of length m, where wildcards (characters that match everything) may be present. In this paper we present a number of complexity results and fast average-case algorithms for pattern matching where wildcards are allowed in the pattern, however, the results are easily adapted to the case where wildcards are allowed in the text as well. We analyse the average-case complexity of these algorithms and derive non-trivial time bounds. These are the first results on the average-case complexity of pattern matching with wildcards which provide a provable separation in time complexity between exact pattern matching and pattern matching with wildcards. We introduce the wc-period of a string which is the period of the binary mask xb where xb[i]=aiffx[i]≠ϕ and b otherwise. We denote the length of the wc-period of a string x by ▪. We show the following results for constant 0<ϵ<1 and a pattern x of length m and g wildcards with ▪ the prefix of length p contains gp wildcards:•If limm→∞⁡gpp=0 there is an optimal algorithm running in O(nlogσ⁡mm)-time on average.•If limm→∞⁡gpp=1−ϵ there is an algorithm running in O(nlogσ⁡mlog2⁡pm)-time on average.•If limm→∞⁡gm=limm→∞⁡1−f(m)=1 any algorithm takes at least Ω(nlogσ⁡mf(m))-time on average.

Adaptive Fuzzy String Matching: How to Merge Datasets with Only One (Messy) Identifying Field

AbstractA single dataset is rarely sufficient to address a question of substantive interest. Instead, most applied data analysis combines data from multiple sources. Very rarely do two datasets contain the same identifiers with which to merge datasets; fields like name, address, and phone number may be entered incorrectly, missing, or in dissimilar formats. Combining multiple datasets absent a unique identifier that unambiguously connects entries is called the record linkage problem. While recent work has made great progress in the case where there are many possible fields on which to match, the much more uncertain case of only one identifying field remains unsolved: this fuzzy string matching problem, both its own problem and a component of standard record linkage problems, is our focus. We design and validate an algorithmic solution called Adaptive Fuzzy String Matching rooted in adaptive learning, and show that our tool identifies more matches, with higher precision, than existing solutions. Finally, we illustrate its validity and practical value through applications to matching organizations, places, and individuals.

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.

Deep String Matching For Duplicate Detection

We consider the problem of duplicate detection in the case where dealing with typographical errors, toponym matching, and datatype dependency are all combined into a single task. We express this task as a string matching problem and resolve it by estimating a conditional probability via an encoder-decoder model, whereby the strings are first encoded with a Deep Recurrent Network into context vectors which are then concatenated and used as inputs for a Deep Classifier Network. We explore the effects that different architectures have on the string matching problem when applied to duplicate detection. Finally, we test the models on numerous datasets of varying size, with some more focused on one of the datatype issues than others.

Entropy-Based Approach in Selection Exact String-Matching Algorithms.

The string-matching paradigm is applied in every computer science and science branch in general. The existence of a plethora of string-matching algorithms makes it hard to choose the best one for any particular case. Expressing, measuring, and testing algorithm efficiency is a challenging task with many potential pitfalls. Algorithm efficiency can be measured based on the usage of different resources. In software engineering, algorithmic productivity is a property of an algorithm execution identified with the computational resources the algorithm consumes. Resource usage in algorithm execution could be determined, and for maximum efficiency, the goal is to minimize resource usage. Guided by the fact that standard measures of algorithm efficiency, such as execution time, directly depend on the number of executed actions. Without touching the problematics of computer power consumption or memory, which also depends on the algorithm type and the techniques used in algorithm development, we have developed a methodology which enables the researchers to choose an efficient algorithm for a specific domain. String searching algorithms efficiency is usually observed independently from the domain texts being searched. This research paper aims to present the idea that algorithm efficiency depends on the properties of searched string and properties of the texts being searched, accompanied by the theoretical analysis of the proposed approach. In the proposed methodology, algorithm efficiency is expressed through character comparison count metrics. The character comparison count metrics is a formal quantitative measure independent of algorithm implementation subtleties and computer platform differences. The model is developed for a particular problem domain by using appropriate domain data (patterns and texts) and provides for a specific domain the ranking of algorithms according to the patterns’ entropy. The proposed approach is limited to on-line exact string-matching problems based on information entropy for a search pattern. Meticulous empirical testing depicts the methodology implementation and purports soundness of the methodology.

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.

Fuzzy String Matching Using a Prefix Table

The string matching problem (that is, the problem of finding all occurrences of a pattern in the text) is one of the well-known problems in symbolic computations with applications in many areas of artificial intelligence. The most famous algorithms for solving it are the finite state machine method and the Knuth-Morris-Pratt algorithm (KMP). In this paper, we consider the problem of finding all occurrences of a fuzzy pattern in the text. Such a pattern is defined as a sequence of fuzzy properties of text characters. To construct a solution to this problem, we introduce a two-dimensional prefix table, which is a generalization of the one-dimensional prefix array used in the KMP algorithm.

Efficient Online String Matching Based on Characters Distance Text Sampling

Searching for all occurrences of a pattern in a text is a fundamental problem in computer science with applications in many other fields, like natural language processing, information retrieval and computational biology. Sampled string matching is an efficient approach recently introduced in order to overcome the prohibitive space requirements of an index construction, on the one hand, and drastically reduce searching time for the online solutions, on the other hand. In this paper we present a new algorithm for the sampled string matching problem, based on a characters distance sampling approach. The main idea is to sample the distances between consecutive occurrences of a given pivot character and then to search online the sampled data for any occurrence of the sampled pattern, before verifying the original text. From a theoretical point of view we prove that, under suitable conditions, our solution can achieve both linear worst-case time complexity and optimal average-time complexity. From a practical point of view it turns out that our solution shows a sub-linear behaviour in practice and speeds up online searching by a factor of up to 9, using limited additional space whose amount goes from 11 to 2.8% of the text size, with a gain up to 50% if compared with previous solutions.

A Chinese String matching Algorithm Based on Edit Distance for Electric Power Customer Service

With the rapid development of information technology, electric power customer service needs to extract accurate information from the data centre to provide customers urgently. String matching is the most straightforward solution. There are some problems in the editing distance definition of traditional string matching algorithm when dealing with Chinese text. In this paper, the pronunciation characteristic of Chinese characters is integrated in the definition of edit distance and a string matching algorithm based on edit distance for electric power customer service data centre is proposed. Finally, through simulation analysis, we demonstrate that this algorithm has good reliability when dealing with Chinese string matching problem. Thus, it is suitable for electric power customer service to obtain the target string.

Модификация алгоритма Валианта для задачи поиска подстрок

The theory of formal languages and, particularly, context-free grammars has been extensively studied and applied in different areas. For example, several approaches to the recognition and classification problems in bioinformatics are based on searching the genomic subsequences possessing some specific features which can be described by a context-free grammar. Therefore, the string-matching problem can be reduced to parsing – verification if some subsequence can be derived in this grammar. Such field of application as bioinformatics requires working with a large amount of data, so it is necessary to improve the existing parsing techniques. The most asymptotically efficient parsing algorithm that can be applied to any context-free grammar is a matrix-based algorithm proposed by Valiant. This paper aims to present Valiant’s algorithm modification, which main advantage is the possibility to divide the parsing table into successively computed layers of disjoint submatrices where each submatrix of the layer can be processed independently. Moreover, our approach is easily adapted for the string-matching problem. Our evaluation shows that the proposed modification retains all benefits of Valiant’s algorithm, especially its high performance achieved by using fast matrix multiplication methods. Also, the modified version decreases a large amount of excessive computations and accelerates the substrings searching.

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.