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The problem of computing the longest common subsequence of two sequences (LCS for short) is a classical and fundamental problem in computer science. In this article, we study four variants of LCS : the Repetition-Bounded Longest Common Subsequence problem (RBLCS), the Multiset-Restricted Common Subsequence problem (MRCS), the Two-Side-Filled Longest Common Subsequence problem (2FLCS), and the One-Side-Filled Longest Common Subsequence problem (1FLCS). Although the original LCS can be solved in polynomial time, all these four variants are known to be NP-hard. Recently, an exact, O (1. 4422 5 n) -time, dynamic programming (DP) based algorithm for RBLCS was proposed, where the two input sequences have lengths n and p o l y (n). Here, we first establish that each of MRCS , 1FLCS , and 2FLCS is polynomially equivalent to RBLCS. Then, we design a refined DP-based algorithm for RBLCS that runs in O (1. 4142 2 n) time, which implies that MRCS , 1FLCS , and 2FLCS can also be solved in O (1. 4142 2 n) time. Finally, we give a polynomial-time 2-approximation algorithm for 2FLCS. [ABSTRACT FROM AUTHOR]

Ribonucleic acid (RNA) structure alignment is an important problem in computational biology to identify structural similarity of RNAs. Obtaining an efficient method for this problem is challenging due to the high computational time for the optimal solution and the low accuracy of a heuristic solution. In this paper, an efficient algorithm is proposed based on a mathematical model called longest arc-preserving common subsequence. The proposed algorithm uses a heuristic technique and high-performance computing to optimize the solution of RNA structure alignment, both in terms of the running time and the accuracy of the output. Extensive experimental studies on a multicore system are conducted to show the effectiveness of the proposed algorithm on two types of data. The first is simulated data that consists of 450 comparisons of RNA structures, while the second is real biological data that consists of 357 comparisons of RNA structures. The results show that the proposed algorithm outperforms the best-known heuristic algorithm in terms of execution time, with a percentage improvement of 71% and increasing the length of the output, i.e., accuracy, by approximately 45% in all studied cases. Finally, future approaches are discussed. [ABSTRACT FROM AUTHOR]

The Internet of Things (IoT) has become a transformative technological infrastructure, serving as a benchmark for automating and standardizing various activities across different domains to reduce human effort, especially in hazardous environments. In these networks, devices with embedded sensors capture valuable information about activities and report it to the nearest server. Although IoT networks are exceptionally useful in solving real-life problems, managing duplicate data values, often captured by neighboring devices, remains a challenging issue. Despite various methodologies reported in the literature to minimize the occurrence of duplicate data, it continues to be an open research problem. This paper presents a sophisticated data aggregation approach designed to minimize the ratio of duplicate data values in the refined set with the least possible information loss in IoT networks. First, at the device level, a local data aggregation process filters out outliers and duplicates data before transmission. Second, at the server level, a dynamic programming-based non-metric method identifies the longest common subsequence (LCS) among data from neighboring devices, which is then shared with the edge module. Simulation results confirm the approach's exceptional performance in optimizing the bandwidth, energy consumption, and response time while maintaining high accuracy and precision, thus significantly reducing overall network congestion. [ABSTRACT FROM AUTHOR]

Ribonucleic acid (RNA) structure alignment is an important problem in computational biology to identify structural similarity of RNAs. Obtaining an efficient method for this problem is challenging due to the high computational time for the optimal solution and the low accuracy of a heuristic solution. In this paper, an efficient algorithm is proposed based on a mathematical model called longest arc-preserving common subsequence. The proposed algorithm uses a heuristic technique and high-performance computing to optimize the solution of RNA structure alignment, both in terms of the running time and the accuracy of the output. Extensive experimental studies on a multicore system are conducted to show the effectiveness of the proposed algorithm on two types of data. The first is simulated data that consists of 450 comparisons of RNA structures, while the second is real biological data that consists of 357 comparisons of RNA structures. The results show that the proposed algorithm outperforms the best-known heuristic algorithm in terms of execution time, with a percentage improvement of 71% and increasing the length of the output, i.e., accuracy, by approximately 45% in all studied cases. Finally, future approaches are discussed.

Time series clustering is the act of grouping time series data without recourse to a label. Algorithms that cluster time series can be classified into two groups: those that employ a time series specific distance measure and those that derive features from time series. Both approaches usually rely on traditional clustering algorithms such as k-means. Our focus is on partitional clustering algorithms that employ elastic distance measures, i.e. distances that perform some kind of realignment whilst measuring distance. We describe nine commonly used elastic distance measures and compare their performance with k-means and k-medoids clusterer. Our findings, based on experiments using the UCR time series archive, are surprising. We find that, generally, clustering with DTW distance is not better than using Euclidean distance and that distance measures that employ editing in conjunction with warping are significantly better than other approaches. We further observe that using k-medoids clusterer rather than k-means improves the clusterings for all nine elastic distance measures. One function, the move–split–merge (MSM) distance, is the best performing algorithm of this study, with time warp edit (TWE) distance a close second. Our conclusion is that MSM or TWE with k-medoids clusterer should be considered as a good alternative to DTW for clustering time series with elastic distance measures. We provide implementations, extensive results and guidance on reproducing results on the associated GitHub repository. [ABSTRACT FROM AUTHOR]

Given several number sequences, determining the longest common subsequence is a classical problem in computer science. This problem has applications in bioinformatics, especially determining transposable genes. Nevertheless, related works only consider how to find one longest common subsequence. In this paper, we consider how to determine the uniqueness of the longest common subsequence. If there are multiple longest common subsequences, we also determine which number appears in all/some/none of the longest common subsequences. We focus on four scenarios: (1) linear sequences without duplicated numbers; (2) circular sequences without duplicated numbers; (3) linear sequences with duplicated numbers; (4) circular sequences with duplicated numbers. We develop corresponding algorithms and apply them to gene sequencing data. [ABSTRACT FROM AUTHOR]

Bus transportation system has become the primary mode of traffic for urban residents. Every day, thousands of buses provide services for millions of passengers. Efficiently monitoring bus trajectories is essential for evaluating service quality and ensuring public safety. In this study, we propose a Flink-based solution to detect anomalies for bus trajectories in real time. Specifically, it can identify two types of anomalies. The first type is when a bus deviates from its designated route during a trip. The second type is when a bus arrives at a scheduled stop along its route but fails to stop. This solution employs CEP (Complex Event Processing) to determine bus arrival events and control the detection process. In this process, it utilizes the state management mechanism to save and update a bus's actual trajectory, which is derived from the raw GPS trajectory and maintained as a stop sequence. Subsequently, it uses LCSS (Longest Common Subsequence) to measure the trajectory similarity between the actual bus trajectory and the scheduled route. We validate the solution using a large-scale real dataset in a Flink cluster with six virtual machines. The experimental results show that (1) each core can handle anomaly detection on 12.5 buses simultaneously and (2) the detection accuracies of the two anomalies are 90.5% and 89.3%, respectively. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer-Aided Design & Computer Graphics / Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We present an efficient algorithm for finding the longest common subsequence of two sequences in cases where the starting points of the sequences are not known. In addition, we differentiate between cases when there can or cannot be assumptions regarding the clustering of the subsequences. [ABSTRACT FROM AUTHOR]

discovering mutations in DNA sequences is the most common approach to diagnosing many genome-related diseases. The optimal alignment of DNA sequences is a reliable approach to discover mutations in one sequence in comparison to the reference sequence. Needleman-Wunsch is the most applicable software for optimal alignment of the sequences and Smith-Waterman is the most applicable one for local optimal alignment of sequences. Their performances are excellent with short sequences, but as the sequences become long their performance degeneration grows exponentially to the point that it is practically impossible to align the sequences such as compete human DNAs. Therefore, many researches are done or being conducted to find ways of performing the alignment with tolerable time and memory consumptions. One such effort is breaking the sequences into same number of parts and align corresponding parts together to produce the overall alignment. With this, there are three achievements simultaneously: run time reduction, main memory utilization reduction, and the possibility to better utilize multiprocessors, multicores and General-Purpose Graphic Processing Units (GPGPUs). In this research, the method for breaking long sequences into smaller parts is based on the divide and conquer approach. The breaking points are selected along the longest common subsequence of the current sequences. The method is evaluated to be very efficient with respect to both time and main memory utilization which are the two confining factors.

The analysis of individuals' movement behaviors is an important area of research in geographic information sciences, with broad applications in smart mobility and transportation systems. Recent advances in information and communication technologies have enabled the collection of vast amounts of mobility data for investigating movement behaviors using trajectory data mining techniques. Trajectory clustering is one commonly used method, but most existing methods require a complete similarity matrix to quantify the similarities among users' trajectories in the dataset. This creates a significant computational overhead for large datasets with many user trajectories. To address this complexity, an efficient clustering-based method for network constraint trajectories is proposed, which can help with transportation planning and reduce traffic congestion on roads. The proposed algorithm is based on spatiotemporal buffering and overlapping operations and involves the following steps: (i) Trajectory preprocessing, which uses an efficient map-matching algorithm to match trajectory points to the road network. (ii) Trajectory segmentation, where a Compressed Linear Reference (CLR) technique is used to convert the discrete 3D trajectories to 2D CLR space. (iii) Spatiotemporal proximity analysis, which calculates a partial similarity matrix using the Longest Common Subsequence similarity indicator in CLR space. (iv) Trajectory clustering, which uses density-based and hierarchical clustering approaches to cluster the trajectories. To verify the proposed clustering-based method, a case study is carried out using real trajectories from the GeoLife project of Microsoft Research Asia. The case study results demonstrate the effectiveness and efficiency of the proposed method compared with other state-of-the-art clustering-based methods. [ABSTRACT FROM AUTHOR]

We consider the classic problem of computing the Longest Common Subsequence (LCS) of two strings of length n. The 40-year-old quadratic-time dynamic programming algorithm has recently been shown to be near-optimal by Abboud, Backurs, and Vassilevska Williams [FOCS'15] and Bringmann and Künnemann [FOCS'15] assuming the Strong Exponential Time Hypothesis. This has led the community to look for subquadratic approximation algorithms for the problem. Yet, unlike the edit distance problem for which a constant-factor approximation in almost-linear time is known, very little progress has been made on LCS, making it a notoriously difficult problem also in the realm of approximation. For the general setting, only a naive O(nɛ/2-approximation algorithm with running time OŠ(n2-ɛ has been known, for any constant 0 < ɛ ≤ 1. Recently, a breakthrough result by Hajiaghayi, Seddighin, Seddighin, and Sun [SODA'19] provided a linear-time algorithm that yields a O(n0.497956-approximation in expectation; improving upon the naive O(√ n)-approximation for the first time. In this paper, we provide an algorithm that in time O(n2-ɛ) computes an OŠ(n2ɛ/5-approximation with high probability, for any 0 < ɛ ≤ 1. Our result (1) gives an OŠ(n0.4-approximation in linear time, improving upon the bound of Hajiaghayi, Seddighin, Seddighin, and Sun, (2) provides an algorithm whose approximation scales with any subquadratic running time O(n2-ɛ), improving upon the naive bound of O(nɛ/2) for any ɛ, and (3) instead of only in expectation, succeeds with high probability. [ABSTRACT FROM AUTHOR]

Copyright of Telecommunication Engineering is the property of Telecommunication Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we revisit the problem of computing longest common almost increasing subsequence (LCAIS) where, given two input sequences, the goal is to compute a common subsequence that is 'almost' increasing. Here the concept of an almost increasing subsequence offers an interesting relaxation over the increasing condition. This problem has been studied in the literature albeit with some constraints. Here, we present a number of a number of algorithmic approaches to solve the problem more generally and efficiently. [ABSTRACT FROM AUTHOR]

Longest common subsequence (LCS) is one of the most fundamental problems in combinatorial optimization. Apart from theoretical importance, LCS has enormous applications in bioinformatics, revision control systems, and data comparison programs. Although a simple dynamic program computes LCS in quadratic time, it has been recently proven that the problem admits a conditional lower bound and may not be solved in truly subquadratic time [2, 18]. In addition to this, LCS is notoriously hard with respect to approximation algorithms. Apart from a trivial sampling technique that obtains an nx approximation solution in time O(n2-2x) nothing else is known for LCS. This is in sharp contrast to its dual problem edit distance, for which several linear time solutions were obtained in the past two decades [5, 6, 10, 11, 19]. In this work, we present the first nontrivial algorithm for approximating LCS in linear time. Our main result is a linear time algorithm for the LCS which has an approximation factor of O(n0.4991319) in expectation. This beats the √n barrier for approximating LCS in linear time. [ABSTRACT FROM AUTHOR]

discovering mutations in DNA sequences is the most common approach to diagnosing many genome-related diseases. The optimal alignment of DNA sequences is a reliable approach to discover mutations in one sequence in comparison to the reference sequence. Needleman-Wunsch is the most applicable software for optimal alignment of the sequences and Smith-Waterman is the most applicable one for local optimal alignment of sequences. Their performances are excellent with short sequences, but as the sequences become long their performance degeneration grows exponentially to the point that it is practically impossible to align the sequences such as compete human DNAs. Therefore, many researches are done or being conducted to find ways of performing the alignment with tolerable time and memory consumptions. One such effort is breaking the sequences into same number of parts and align corresponding parts together to produce the overall alignment. With this, there are three achievements simultaneously: run time reduction, main memory utilization reduction, and the possibility to better utilize multiprocessors, multicores and General-Purpose Graphic Processing Units (GPGPUs). In this research, the method for breaking long sequences into smaller parts is based on the divide and conquer approach. The breaking points are selected along the longest common subsequence of the current sequences. The method is evaluated to be very efficient with respect to both time and main memory utilization which are the two confining factors. [ABSTRACT FROM AUTHOR]

The longest common palindromic subsequence (LCPS) problem is a variant of the longest common subsequence (LCS) problem. Given two input sequences A and B , the LCPS problem is to find the common subsequence of A and B such that the answer is a palindrome with the maximal length. The LCPS problem was first proposed by Chowdhury et al. (2014) [9] , who proposed a dynamic programming algorithm with O (m 2 n 2) time, where m and n denote the lengths of A and B , respectively. This paper proposes a diagonal-based algorithm for solving the LCPS problem with O (L (m − L) R log ⁡ n) time and O (R L) space, where R denotes the number of match pairs between A and B , and L denotes the LCPS length. In our algorithm, the 3-dimensional minima finding algorithm is invoked to overcome the domination problem. As experimental results show, our algorithm is efficient practically compared with some previously published algorithms. [ABSTRACT FROM AUTHOR]

The manual process of scoring short answers of Arabic essay questions is exhaustive, susceptible to error and consumes instructor’s time and resources. This paper explores longest common subsequence (LCS) algorithm as a string-based text similarity measure for effectively scoring short answers of Arabic essay questions. To achieve this effectiveness, the longest common subsequence is modified by developing weight-based measurement techniques and implemented along with using Arabic WordNet for scoring Arabic short answers. The experiments conducted on a dataset of 330 students’ answers reported Root Mean Square Error (RMSE) value of 0.81 and Pearson correlation r value of 0.94. Findings based on experiments have shown improvements in the accuracy of performance of the proposed approach compared to similar studies. Moreover, the statistical analysis has shown that the proposed method scores students’ answers similar to that of human estimator.

The longest common subsequence (LCS) length of two strings is used as one of the most fundamental metrics measuring the similarity between the strings. To find out the local structures common to the strings under this similarity metric, we need a fast calculation of the LCS length of any pair of substrings of the two strings. For supporting such queries, it makes sense to preprocess the two strings in a quadratic time, because it takes about the same amount of time to compute the LCS length of the entire strings from scratch. We propose a quadratic-time constructible data structure that supports sublinear-time queries of the LCS length for any pair of substrings. The query time is O (l log 1 + ϵ ⁡ l) , where ϵ is a positive constant arbitrarily small and l is the sum of the substring lengths. [ABSTRACT FROM AUTHOR]

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The existing multi-source contour matching studies have focused on the matching methods with consideration of topological relations and similarity measurement based on spatial Euclidean distance, while it is lack of taking the contour geometric features into account, which may lead to mismatching in map boundaries and areas with intensive contours or extreme terrain changes. In light of this, it is put forward that a matching strategy from coarse to precious based on the contour geometric features. The proposed matching strategy can be described as follows. Firstly, the point sequence is converted to feature sequence according to a feature descriptive function based on curvature and angle of normal vector. Then the level of similarity among multi-source contours is calculated by using the longest common subsequence solution. Accordingly, the identical contours could be matched based on the above calculated results. In the experiment for the proposed method, the reliability and efficiency of the matching method are verified using simulative datasets and real datasets respectively. It has been proved that the proposed contour matching strategy has a high matching precision and good applicability.

Discretization and feature selection are two relevant techniques for dimensionality reduction. The first one aims to transform a set of continuous attributes into discrete ones, and the second removes the irrelevant and redundant features; these two methods often lead to be more specific and concise data. In this paper, we propose to simultaneously deal with optimal feature subset selection, discretization, and classifier parameter tuning. As an illustration, the proposed problem formulation has been addressed using a constrained many-objective optimization algorithm based on dominance and decomposition (C-MOEA/DD) and a limited-memory implementation of the warping longest common subsequence algorithm (WarpingLCSS). In addition, the discretization sub-problem has been addressed using a variable-length representation, along with a variable-length crossover, to overcome the need of specifying the number of elements defining the discretization scheme in advance. We conduct experiments on a real-world benchmark dataset; compare two discretization criteria as discretization objective, namely Ameva and ur-CAIM; and analyze recognition performance and reduction capabilities. Our results show that our approach outperforms previous reported results by up to 11% and achieves an average feature reduction rate of 80%. [ABSTRACT FROM AUTHOR]

Given a mathematical expression in LaTeX or MathML format, retrieval algorithm extracts similar expressions from a database. In our previous work, we have used Longest Common Subsequence (LCS) algorithm to match two expressions of lengths, m and n , which takes O (m n) time complexity. If there are T database expressions, total complexity is O (T m n) , and an increase in T also increases this complexity. In the present work, we propose to use parallel LCS algorithm in our retrieval process. Parallel LCS has O (max (m , n)) time complexity with max (m , n) processors and total complexity can be reduced to O (T max (m , n)). For our experimentation, OpenMP based implementation has been used on Intel i 3 processor with 4 cores. However, for smaller expressions, parallel version takes more time as the implementation overhead dominates the algorithmic improvement. As such, we have proposed to use parallel version, selectively, only on larger expressions, in our retrieval algorithm to achieve better performance. We have compared the sequential and parallel versions of our ME retrieval algorithm, and the performance results have been reported on a database of 829 mathematical expressions. [ABSTRACT FROM AUTHOR]

Summary: This article presents a high‐level synthesis implementation of the longest common subsequence (LCS) algorithm combined with a weighted‐based scheduler for comparing biological sequences prioritizing energy consumption or execution time. The LCS algorithm has been thoroughly tailored using Vivado High‐Level Synthesis tool, which is able to synthesize register transfer level (RTL) from high‐level language descriptions, such as C/C++. Performance and energy consumption results were obtained with a CPU Intel Core i7‐3770 CPU and an Alpha‐Data ADM‐PCIE‐KU3 board that has a Xilinx Kintex UltraScale XCKU060 FPGA chip. We executed a batch of 20 comparisons of sequences on 10k, 20k, and 50k sizes. Our experiments showed that the energy consumption on the combined approach was significantly lower when compared to the CPU, achieving 75% energy reduction on 50k comparisons. We also used the tool proposed in this article to do a case study on Covid‐19, with real SARS‐CoV‐2 sequences, comparing their LCS scores. [ABSTRACT FROM AUTHOR]

Aiming at the problem that the traditional similarity measurement methods cannot effectively measure the similarity of the time series with the difference both in the trend and detail, this paper proposes a new time series similarity measurement method (MP-SAX) based on the morphological pattern (MP) and symbolic aggregate approximation (SAX). According to the empirical mode decomposition (EMD), the time series are decomposed and reconstructed into the trend component and the detail component. Then, the similarity of the trend component under morphological pattern coding and that of the detail component under symbolic aggregate approximation coding are respectively calculated by the longest common subsequence (LCS). Finally, the similarity of the time series is obtained by weighted aggregation of the similarity of trend component and detail component. The MP-SAX is verified by the simulation time series and the time series from UCR Time Series Classification/Clustering Homepage. The results show that the MP-SAX can effectively measure the similarity of the time series with the changes both in trend and detail.

The similarity of two one-dimensional sequences is usually measured by the longest common subsequence (LCS) algorithms. However, these algorithms cannot be directly extended to solve the two or higher dimensional data. Thus, for the two-dimensional data, computing the similarity with an LCS-like approach remains worthy of investigation. In this paper, we utilize a systematic way to give the generalized definition of the two-dimensional largest common substructure (TLCS) problem by referring to the traditional LCS concept. With various matching rules, eight possible versions of TLCS problems may be defined. However, only four of them are shown to be valid. We prove that all of these four TLCS problems are NP -hard and APX -hard. To accomplish the proofs, two of the TLCS problems are reduced from the 3-satisfiability problem, and the other two are reduced from the 3-dimensional matching problem. [ABSTRACT FROM AUTHOR]

With the rapid development of intelligent transportation, how to generate high ⁃ precision maps based on vehicle trajectory data has become a major problem in the industry. Trajectory similarity calcula⁃ tion and similar trajectory extraction are important steps to use the similar trajectory to infer the remaining lane position, and its correction greatly affects the accuracy of the lane position. The traditional LCSS (lon⁃ gest common subsequence) algorithm is mostly used to calculate the similarity of overlapping trajectories. To solve this problem, according to the characteristics that the lane trajectories are parallel and maintain a fixed distance, an improved LCSS method is proposed. Firstly, the buffer is constructed to screen out simi⁃ lar trajectories, then the trajectory alignment strategy based on translation and resampling is used to synchro⁃ nize the two trajectories in space and time. Finally, the similarity of the two trajectories is calculated based on LCSS. When the similarity satisfies the threshold condition, it is determined that the trajectory pairs are similar. Experiment results show that the proposed method can effectively extract similar trajectories. [ABSTRACT FROM AUTHOR]

Discretization and feature selection are two relevant techniques for dimensionality reduction. The first one aims to transform a set of continuous attributes into discrete ones, and the second removes the irrelevant and redundant features; these two methods often lead to be more specific and concise data. In this paper, we propose to simultaneously deal with optimal feature subset selection, discretization, and classifier parameter tuning. As an illustration, the proposed problem formulation has been addressed using a constrained many-objective optimization algorithm based on dominance and decomposition (C-MOEA/DD) and a limited-memory implementation of the warping longest common subsequence algorithm (WarpingLCSS). In addition, the discretization sub-problem has been addressed using a variable-length representation, along with a variable-length crossover, to overcome the need of specifying the number of elements defining the discretization scheme in advance. We conduct experiments on a real-world benchmark dataset; compare two discretization criteria as discretization objective, namely Ameva and ur-CAIM; and analyze recognition performance and reduction capabilities. Our results show that our approach outperforms previous reported results by up to 11% and achieves an average feature reduction rate of 80%.