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Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm to solve combinatorial optimization problems in the era of noisy intermediate-scale quantum computers. Recently it has been revealed that warm-start approaches can improve the performance of QAOA, where approximate solutions are obtained by classical algorithms in advance and incorporated into the initial state and/or unitary ansatz. In this work, we study in detail how the accuracy of approximate solutions affects the performance of the warm-start QAOA (WS-QAOA). We numerically find that in typical MAX-CUT problems, WS-QAOA achieves higher fidelity (probability that exact solutions are observed) and approximation ratio than QAOA as the Hamming distance of approximate solutions to the exact ones becomes smaller. We reveal that this could be quantitatively attributed to the initial state of the ansatz. We also solve MAX-CUT problems by WS-QAOA with approximate solutions obtained via QAOA, having higher fidelity and approximation ratio than QAOA especially when the circuit is relatively shallow. We believe that our study may deepen understanding of the performance of WS-QAOA and also provide a guide as to the necessary quality of approximate solutions. [ABSTRACT FROM AUTHOR]

Sequence motif discovery algorithms enhance the identification of novel deoxyribonucleic acid sequences with pivotal biological significance, especially transcription factor (TF)-binding motifs. The advent of assay for transposase-accessible chromatin using sequencing (ATAC-seq) has broadened the toolkit for motif characterization. Nonetheless, prevailing computational approaches have focused on delineating TF-binding footprints, with motif discovery receiving less attention. Herein, we present Cis rEgulatory Motif Influence using de Bruijn Graph (CEMIG), an algorithm leveraging de Bruijn and Hamming distance graph paradigms to predict and map motif sites. Assessment on 129 ATAC-seq datasets from the Cistrome Data Browser demonstrates CEMIG's exceptional performance, surpassing three established methodologies on four evaluative metrics. CEMIG accurately identifies both cell-type-specific and common TF motifs within GM12878 and K562 cell lines, demonstrating its comparative genomic capabilities in the identification of evolutionary conservation and cell-type specificity. In-depth transcriptional and functional genomic studies have validated the functional relevance of CEMIG-identified motifs across various cell types. CEMIG is available at https://github.com/OSU-BMBL/CEMIG , developed in C++ to ensure cross-platform compatibility with Linux, macOS and Windows operating systems. [ABSTRACT FROM AUTHOR]

This paper presents a method for unsupervised classification of entities by a group of agents with unknown domains and levels of expertise. In contrast to the existing methods based on majority voting ("wisdom of the crowd") and their extensions by expectation-maximization procedures, the suggested method first determines the levels of the agents' expertise and then weights their opinions by their expertise level. In particular, we assume that agents will have relatively closer classifications in their field of expertise. Therefore, the expert agents are recognized by using a weighted Hamming distance between their classifications, and then the final classification of the group is determined from the agents' classifications by expectation-maximization techniques, with preference to the recognized experts. The algorithm was verified and tested on simulated and real-world datasets and benchmarked against known existing algorithms. We show that such a method reduces incorrect classifications and effectively solves the problem of unsupervised collaborative classification under uncertainty, while outperforming other known methods. [ABSTRACT FROM AUTHOR]

We thoroughly study a novel but basic combinatorial matrix completion problem: Given a binary incomplete matrix, fill in the missing entries so that every pair of rows in the resulting matrix has a Hamming distance within a specified range. We obtain an almost complete picture of the complexity landscape regarding the distance constraints and the maximum number of missing entries in any row. We develop polynomial-time algorithms for maximum diameter three based on Deza's theorem (1973) [11] from extremal set theory. We also prove NP-hardness for diameter at least four. For the number of missing entries per row, we show polynomial-time solvability when there is only one and NP-hardness when there can be at least two. In many of our algorithms, we heavily rely on Deza's theorem to identify sunflower structures. This paves the way towards polynomial-time algorithms which are based on finding graph factors and solving 2-SAT instances. [ABSTRACT FROM AUTHOR]

Motivation Comparing single-stranded nucleic acids (ssNAs) secondary structures is fundamental when investigating their function and evolution and predicting the effect of mutations on their structures. Many comparison metrics exist, although they are either too elaborate or not sensitive enough to distinguish close ssNAs structures. Results In this context, we developed AptaMat, a simple and sensitive algorithm for ssNAs secondary structures comparison based on matrices representing the ssNAs secondary structures and a metric built upon the Manhattan distance in the plane. We applied AptaMat to several examples and compared the results to those obtained by the most frequently used metrics, namely the Hamming distance and the RNAdistance, and by a recently developed image-based approach. We showed that AptaMat is able to discriminate between similar sequences, outperforming all the other here considered metrics. In addition, we showed that AptaMat was able to correctly classify 14 RFAM families within a clustering procedure. Availability and implementation The python code for AptaMat is available at https://github.com/GEC-git/AptaMat.git. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

The affine scale-invariant feature transform (ASIFT) algorithm is a feature extraction algorithm with affinity and scale invariance, which is suitable for image feature matching using unmanned aerial vehicles (UAVs). However, there are many problems in the matching process, such as the low efficiency and mismatching. In order to improve the matching efficiency, this algorithm firstly simulates image distortion based on the position and orientation system (POS) information from real-time UAV measurements to reduce the number of simulated images. Then, the scale-invariant feature transform (SIFT) algorithm is used for feature point detection, and the extracted feature points are combined with the binary robust invariant scalable keypoints (BRISK) descriptor to generate the binary feature descriptor, which is matched using the Hamming distance. Finally, in order to improve the matching accuracy of the UAV images, based on the random sample consensus (RANSAC) a false matching eliminated algorithm is proposed. Through four groups of experiments, the proposed algorithm is compared with the SIFT and ASIFT. The results show that the algorithm can optimize the matching effect and improve the matching speed. [ABSTRACT FROM AUTHOR]

Trace reconstruction considers the task of recovering an unknown string $\mathbf {x}\in \{0,1\}^{n}$ given a number of independent “traces”, i.e., subsequences of $\mathbf {x}$ obtained by randomly and independently deleting every symbol of $\mathbf {x}$ with some probability $p$. The information-theoretic limit of the number of traces needed to recover a string of length $n$ is still unknown. This limit is essentially the same as the number of traces needed to determine, given strings $\mathbf {x}$ and $\mathbf {y}$ and traces of one of them, which string is the source. The most-studied class of algorithms for the worst-case version of the problem are “mean-based” algorithms. These are a restricted class of distinguishers that only use the mean value of each coordinate on the given samples. In this work we study limitations of mean-based algorithms on strings at small Hamming or edit distance. We show that, on the one hand, distinguishing strings that are nearby in Hamming distance is “easy” for such distinguishers. On the other hand, we show that distinguishing strings that are nearby in edit distance is “hard” for mean-based algorithms. Along the way, we also describe a connection to the famous Prouhet-Tarry-Escott (PTE) problem, which shows a barrier to finding explicit hard-to-distinguish strings: namely such strings would imply explicit short solutions to the PTE problem, a well-known difficult problem in number theory. Furthermore, we show that the converse is also true, thus, finding explicit solutions to the PTE problem is equivalent to the problem of finding explicit strings that are hard-to-distinguish by mean-based algorithms. Our techniques rely on complex analysis arguments that involve careful trigonometric estimates, and algebraic techniques that include applications of Descartes’ rule of signs for polynomials over the reals. [ABSTRACT FROM AUTHOR]

To solve the low accuracy of image feature matching in horticultural robot visual navigation, an innovative and effective image feature matching algorithm was proposed combining the improved Oriented FAST and Rotated BRIEF (ORB) and Lucas–Kanade (LK) optical flow algorithm. First, image feature points were extracted according to the adaptive threshold calculated using the Michelson contrast. Then, the extracted feature points were uniformed by the quadtree structure, which can reduce the calculated amount of feature matching, and the uniform ORB feature points were roughly matched to estimate the position of the feature points in the matched image using the improved LK optical flow. Finally, the Hamming distance between rough matching points was calculated for precise matching. Feature extraction and matching experiments were performed in four typical scenes: normal light, low light, high texture, and low texture. Compared with the traditional algorithm, the uniformity and accuracy of the feature points extracted by the proposed algorithm were enhanced by 0.22 and 50.47%, respectively. Meanwhile, the results revealed that the matching accuracy of the proposed algorithm increased by 14.59%, whereas the matching time and total time decreased by 39.18% and 44.79%, respectively. The proposed algorithm shows great potential for application in the visual simultaneous localization and mapping (V-SLAM) of horticultural robots to achieve higher accuracy of real-time positioning and map construction. [ABSTRACT FROM AUTHOR]

The rapid and accurate identification of photovoltaic (PV) model parameters is of great significance in solving practical engineering problems such as PV power prediction, maximum power point tracking and battery failure model recognition. Aiming at the shortcomings of low accuracy and poor reliability and being easy to fall into local optimization when standard intelligent optimization algorithms identify PV model parameters, a novel drunken adaptive walking chaotic wolf swarm algorithm is proposed, which is named DCWPA for short. The DCWPA uses the chaotic map sequence to initialize the population, thus to improve the diversity of the initial population. It adopts the walking direction mechanism based on the drunk walking model and the adaptive walking step size to increase the randomness of walking, enhance the individual's ability to explore and develop and improve the ability of algorithm optimization. It also designs the judgment conditions for half siege in order to accelerate the convergence of the algorithm and improve the speed of the algorithm. In the iterative process, according to the change of the optimal solution, the Hamming Distance is used to judge the similarity of individuals in the population, and the individuals in the population are constantly updated to avoid the algorithm from stopping evolution prematurely due to falling into local optimization. This paper firstly analyzes the time complexity of the algorithm, and then selects eight standard test functions (Benchmark) with different characteristics to verify the performance of the DCWPA algorithm for continuous optimization, and finally the improved algorithm is applied for parameter identification of PV models. The experiments show that the DCWPA has higher identification accuracy than other algorithms, and the results are more consistent with the measured data. Thus, the effectiveness and superiority of the improved algorithm in identifying solar cell parameters are verified, and the identification effect of the improved algorithm on solar cell parameters under different illumination is shown. This research provides a new idea and method for parameter identification of a PV module model. [ABSTRACT FROM AUTHOR]

An improved ORB feature point purification method has been proposed to address the problem of large feature point matching error and low image registration rate in the oriented FAST and rotated BRIEF (ORB) feature point color image matching algorithm. Pure virtual quaternions were used to represent the color image pixels in this method, and an improved FAST algorithm was used to detect the color feature points at first. The firework algorithm has been used to divide the detected feature points into key areas, auxiliary areas, and small influence areas, depending on the degree of attachment. The feature points of the key area and the subsidiary area are the required feature points. In order to further improve the efficiency of matching the color image feature points, the firework explosion radius formula and the explosion number formula in the firework algorithm have been improved, and an improved firework algorithm is proposed. This improved algorithm purifies the quaternion-represented color image feature points. For feature matching, the hamming distance was used. Experiments show that, when compared to the traditional ORB algorithm, the improved algorithm retains the key feature points of the color image with high accuracy, removes a large number of irrelevant feature points and noise points, and provides significantly higher accuracy and efficiency of color image matching. [ABSTRACT FROM AUTHOR]

Line-of-sight (LOS) is a critical requirement for mmWave wireless communications. In this work, we explore the use of access point (AP) infrastructure mobility to optimize indoor mmWave WiFi network performance based on the discovery of LOS connectivity to stations (STAs). We consider a ceiling-mounted mobile (CMM) AP as the infrastructure mobility framework. Within this framework, we propose two heuristic algorithms (basic and weighted) derived from Hamming distance computation and a machine learning (ML) solution fully exploiting available network state information to address the LOS discovery problem. Based on the ML solution, we then propose a systematic solution WiMove , which can decide if and where the AP should move to for optimizing network performance. Using both ns-3 based simulation and experimental prototype implementation, we show that the throughput and fairness performance of WiMove is up to 119% and 15% better compared with single static AP and brute force search. • We focus on line of sight discovery for mmWave WiFi with access point mobility. • We propose two heuristic algorithms and a machine learning (ML) solution. • Based on the ML solution, we provide a systematic solution called WiMove. • WiMove outperforms conventional methods (e.g., static AP and brute force). [ABSTRACT FROM AUTHOR]

Due to the advantage of capacity-achieving, polar codes have been extended to the block fading channel whereas most constructions involve complex iterative-calculation. In this paper, we establish a systematic framework to analyze the error performance of polar codes in the case of block mapping and random mapping. For both the mappings, by introducing the new concept, named split polar spectrum, we derive the upper bound on the error probability of polarized channel which explicitly reveals the relationship between the diversity order $L$ and the block-wise weight distribution of the codeword. For the special case $L=2$ in the block mapping, we design the enumeration algorithm to calculate the exact split polar spectrum based on the general MacWilliams identities. For arbitrary diversity order in the random mapping, with the help of uniform interleaving, we derive the approximate split polar spectrum by combining the polar spectrum and the probability of fading pattern for a specific weight. Furthermore, we propose the design criteria to construct polar codes over the block fading channel. The full diversity criterion is the primary target to achieve the diversity gain and the product distance criterion requires to maximize the product of the block-wise Hamming distance whereby obtain the coding gain. Guided by these design criteria, the construction metrics, respectively named polarized diversity weight (PDW) and simplified PDW (SPDW) are proposed to designpolar codes in both mappings. Such simple metrics can construct polar codes with similar or better performance over those based on traditional methods in block fading channel. [ABSTRACT FROM AUTHOR]

In order to satisfy the rapidly increasing demand for data volume, large data center networks (DCNs) have been proposed. In 2019, Zhang et al. proposed a new highly scalable DCN architecture named HSDC (Highly Scalable Data Center Network), which can achieve greater incremental scalability. In this paper, we give the definition of the logical graph of HSDC, named H n , which can be treated as a compound graph of hypercube and complete graph of the same dimension. First, we prove that the connectivity and tightly super connectivity of H n are both n. Then, we give an O(n) shortest unicast algorithm to find a shortest path between any two distinct nodes in H n , and prove the correctness of this algorithm. In fact, we also prove that the length of the shortest path constructed by this algorithm is no more than 2 d + 1 if d < n and at most 2d if d = n , where d is the Hamming distance between the start and end nodes, and the diameter of H n is 2n. [ABSTRACT FROM AUTHOR]

The development of information technology has produced massive amounts of data, which has brought severe challenges to information storage. Traditional electronic storage media cannot keep up with the ever-increasing demand for data storage, but in its place DNA has emerged as a feasible storage medium with high density, large storage capacity and strong durability. In DNA data storage, many different approaches can be used to encode data into codewords. DNA coding is a key step in DNA storage and can directly affect storage performance and data integrity. However, since errors are prone to occur in DNA synthesis and sequencing, and non-specific hybridization is prone to occur in the solution, how to effectively encode DNA has become an urgent problem to be solved. In this article, we propose a DNA storage coding method based on the equilibrium optimization random search (EORS) algorithm, which meets the Hamming distance, GC content and no-runlength constraints and can reduce the error rate in storage. Simulation experiments have shown that the size of the DNA storage code set constructed by the EORS algorithm that meets the combination constraints has increased by an average of 11% compared with previous work. The increase in the code set means that shorter DNA chains can be used to store more data. [ABSTRACT FROM AUTHOR]

Graphs such as de Bruijn graphs and OLC (overlap-layout-consensus) graphs have been widely adopted for the de novo assembly of genomic short reads. This work studies another important problem in the field: how graphs can be used for high-performance compression of the large-scale sequencing data. We present a novel graph definition named Hamming-Shifting graph to address this problem. The definition originates from the technological characteristics of next-generation sequencing machines, aiming to link all pairs of distinct reads that have a small Hamming distance or a small shifting offset or both. We compute multiple lexicographically minimal k-mers to index the reads for an efficient search of the weight-lightest edges, and we prove a very high probability of successfully detecting these edges. The resulted graph creates a full mutual reference of the reads to cascade a code-minimized transfer of every child-read for an optimal compression. We conducted compression experiments on the minimum spanning forest of this extremely sparse graph, and achieved a 10 − 30% more file size reduction compared to the best compression results using existing algorithms. As future work, the separation and connectivity degrees of these giant graphs can be used as economical measurements or protocols for quick quality assessment of wet-lab machines, for sufficiency control of genomic library preparation, and for accurate de novo genome assembly. Author summary: We present a novel graph-based algorithm to compress next-generation short sequencing reads. The novelty of the algorithm is attributed to a new definition of genomic sequence graph named Hamming-Shifting graph. It consists of edges between distinct reads that have a small Hamming distance or a small shifting offset or both. Efficient construction of Hamming-Shifting graphs is challenging. We introduce a heuristic technique to detect the weight-lightest edges through multiple minimizers from each read, then search the minimum spanning trees and forests of the Hamming-Shifting graph for a high-performance compression of the reads. Our method achieves an additional 10 − 30% file size reduction compared to contemporary compression techniques. [ABSTRACT FROM AUTHOR]

This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming distance from codeword estimates to the received sequence in the reprocessing stages of the OSD algorithm. We prove that the Hamming distance and weighted Hamming distance distributions can be characterized as mixture models capturing the decoding error probability and code weight enumerator. Simulation and numerical results show that our proposed statistical approaches can accurately describe the distance distributions. Based on these distributions and with the aim to reduce the decoding complexity, several techniques, including stopping rules and discarding rules, are proposed, and their decoding error performance and complexity are accordingly analyzed. Simulation results for decoding various eBCH codes demonstrate that the proposed techniques can significantly reduce the decoding complexity with a negligible loss in the decoding error performance. [ABSTRACT FROM AUTHOR]

We consider the circular pattern matching with k mismatches (k -CPM) problem in which one is to compute the minimal Hamming distance of every length- m substring of T and any cyclic rotation of P , if this distance is no more than k. It is a variation of the well-studied k -mismatch problem. A multitude of papers has been devoted to solving the k -CPM problem, but only average-case upper bounds are known. In this paper, we present the first non-trivial worst-case upper bounds for this problem. Specifically, we show an O (n k) -time algorithm and an O (n + n m k 4) -time algorithm. The latter algorithm applies in an extended way a technique that was very recently developed for the k -mismatch problem Bringmann et al. (2019) [10]. A preliminary version of this work appeared at FCT 2019 [35]. In this version we improve the time complexity of the second algorithm from O (n + n m k 5) to O (n + n m k 4). [ABSTRACT FROM AUTHOR]

The Oriented FAST and Rotated BRIEF (ORB) algorithm has the problem that the extracted feature points are overconcentrated or even overlapped, leading to information loss of local image features. A homogenized ORB algorithm using dynamic thresholds and improved quadtree method is proposed in this paper, named Quadtree ORB (QTORB). In the feature point extraction stage, a new dynamic local threshold calculation method is proposed to enhance the algorithm's ability to extract feature points at homogeneous regions. Then, a quadtree method is improved and adopted to manage and optimize feature points to eliminate those excessively concentrated and overlapping feature points. Meanwhile, in the feature points optimization process, different quadtree depths are set at different image pyramid levels to prevent excessive splitting of the quadtree and increase calculation speed. In the feature point description stage, local gray difference value information is introduced to enhance the saliency of the feature description. Finally, the Hamming distance is used to match points and RANSAC is used to avoid mismatches. Two datasets, namely, the optical image dataset and SAR image dataset, are used in the experiment. The experimental result shows that, considering accuracy and real-time efficiency, the QTORB can effectively improve the distribution uniformity of feature points. [ABSTRACT FROM AUTHOR]

Background: The Damerau-Levenshtein (DL) distance metric has been widely used in the biological science. It tries to identify the similar region of DNA,RNA and protein sequences by transforming one sequence to the another using the substitution, insertion, deletion and transposition operations. Lowrance and Wagner have developed an O(mn) time O(mn) space algorithm to find the minimum cost edit sequence between strings of length m and n, respectively. In our previous research, we have developed algorithms that run in O(mn) time using only O(s∗min{m,n}+m+n) space, where s is the size of the alphabet comprising the strings, to compute the DL distance as well as the corresponding edit sequence. These are so far the fastest and most space efficient algorithms. In this paper, we focus on the development of algorithms whose asymptotic space complexity is linear. Results: We develop linear space algorithms to compute the Damerau-Levenshtein (DL) distance between two strings and determine the optimal trace (corresponding edit operations.)Extensive experiments conducted on three computational platforms–Xeon E5 2603, I7-x980 and Xeon E5 2695–show that, our algorithms, in addition to using less space, are much faster than earlier algorithms. Conclusion: Besides using less space than the previously known algorithms,significant run-time improvement was seen for our new algorithms on all three of our experimental platforms. On all platforms, our linear-space cache-efficient algorithms reduced run time by as much as 56.4% and 57.4% in respect to compute the DL distance and an optimal edit sequences compared to previous algorithms. Our multi-core algorithms reduced the run time by up to 59.3% compared to the best previously known multi-core algorithms. [ABSTRACT FROM AUTHOR]

The huge amount of data acquired by high-throughput sequencing requires data reduction for effective analysis. Here we give a clustering algorithm for genome-wide open chromatin data using a new data reduction method. This method regards the genome as a string of 1s and 0s based on a set of peaks and calculates the Hamming distances between the strings. This algorithm with the systematically optimized set of peaks enables us to quantitatively evaluate differences between samples of hematopoietic cells and classify cell types, potentially leading to a better understanding of leukemia pathogenesis. Author summary: High-throughput sequencing provides us huge amounts of data about gene regulation. In order to extract useful information from the data, data reduction is needed. Although RNA-seq data analysis has been extensively studied, where the focus is mainly on genetic loci, tools for epigenetic sequencing data, such as ATAC-seq data which represent chromatin accessibility, are comparatively lacking. Since the binding of transcription factors mainly occurs in open chromatin regions, it is presumably important to understand how chromatin accessibility landscape affects cell phenotype. In this context, we developed a systematic algorithm to select a set of peaks representing the open state of chromatin for a given sample of ATAC-seq data. This algorithm quantifies the difference between samples by regarding the genome as a string of 1s and 0s with Hamming distances and then performs hierarchical clustering. This algorithm has less computational cost and gives a reasonable cell type classification compared to a previous method. In this work, as an application of this algorithm, we present a comparative analysis of leukemia samples with healthy hematopoietic cells and provide new insights about the relationship between chromatin structures, cell surface proteins, and symptoms in leukemia. [ABSTRACT FROM AUTHOR]

In the nonbinary low-density parity check (NB-LDPC) codes decoding algorithms, the iterative hard reliability based on majority logic decoding (IHRB-MLGD) algorithm has poor error correction performance. The essential reason is that the hard information is used in the initialization and iterative processes. For the problem of partial loss of information, when the reliability is assigned during initialization, the error correction performance is improved by modifying the assignment of reliability at initialization. The initialization process is determined by the probability of occurrence of the number of erroneous bits in the symbol and the Hamming distance. In addition, the IHRB-MLGD decoding algorithm uses the hard decision in the iterative decoding process. The improved algorithm adds soft decision information in the iterative process, which improves the error correction performance while only slightly increasing the decoding complexity, and improves the reliability accumulation process which makes the algorithm more stable. The simulation results indicate that the proposed algorithm has a better decoding performance than IHRB algorithm. [ABSTRACT FROM AUTHOR]

Effective resistance to intellectual property (IP) piracy, overproduction and reverse engineering are becoming more and more necessary in the integrated circuit (IC) supply chain. To protect the hardware, the obfuscation methodology hides the original function by adding a large number of redundant states. However, existing hardware obfuscation approaches have hardware overhead and efficiency of obfuscation limitations. This paper proposed a novel methodology for IP security using the minimum spanning tree finite state machine (MST-FSM) obfuscation. In the minimum spanning tree (MST) algorithm, the Hamming distance defines the cost of obfuscated states. The Kruskal algorithm optimizes the connection relationship of obfuscated states by computing the Hamming distance of the MST-FSM. The proposed MST-FSM is automatically generated and embedded in the hardware IP with the self-building program. Finally, the MST-FSM is applied on the itc99 benchmark circuits and encryption standard IP cores. Compared with other state-of-the-arts, the obfuscation potency is improved by 3.57%, and the average hardware cost is decreased by about 6.01%. [ABSTRACT FROM AUTHOR]

It was demonstrated that, as a nonlinear implementation of Slepian-Wolf Coding, Distributed Arithmetic Coding (DAC) outperforms traditional Low-Density Parity-Check (LPDC) codes for short code length and biased sources. This fact triggers research efforts into theoretical analysis of DAC. In our previous work, we proposed two analytical tools, Codebook Cardinality Spectrum (CCS) and Hamming Distance Spectrum, to analyze DAC for independent and identically-distributed (i.i.d.) binary sources with uniform distribution. This article extends our work on CCS from uniform i.i.d. binary sources to biased i.i.d. binary sources. We begin with the final CCS and then deduce each level of CCS backwards by recursion. The main finding of this article is that the final CCS of biased i.i.d. binary sources is not uniformly distributed over [0, 1). This article derives the final CCS of biased i.i.d. binary sources and proposes a numerical algorithm for calculating CCS effectively in practice. All theoretical analyses are well verified by experimental results. [ABSTRACT FROM AUTHOR]

The computational efficiency of large-scale unit commitment (UC) is still a critical issue in power system and electricity market operations. To reduce the computation time of UC, relaxation-based neighborhood search (RBNS) and improved relaxation inducement (IRI) are proposed in this article. RBNS explores the neighborhood of the linear program (LP) relaxation optimal solution for a high-quality feasible solution. A new distance function, termed relaxation distance (RD), is proposed to measure the distance between the current solution and the tendency of the LP relaxation optimal solution. RBNS can substantially reduce the optimization space, and thus improve the efficiency. IRI has been developed to effectively induce binary variables towards the tendency of the relaxed solution. In contrast to a conventional relaxation inducement method, the binary variables are symmetrically and bi-directionally induced. The ratio between the inducing functions and the original objective function is optimized. IRI can induce more binary variables to integrality, and fewer binary variables need to be branched. Therefore, the size of the branch-and-bound tree can be reduced significantly. Modified IEEE-300 bus system and Polish 2746 bus system are used to demonstrate the effectiveness and performance of the proposed RBNS and IRI methods. [ABSTRACT FROM AUTHOR]

In a real-world cloud server, a speech signal is prone to suffer various attacks, such as malicious muting and tampering. In such a context, the privacy security of the speech owner will not be guaranteed. In order to achieve content authentication of encrypted speech in the cloud server, an efficient encrypted speech authentication method based on uniform subband spectrum variance and perceptual hashing is proposed. Firstly, the original speech is scrambled by Henon mapping to construct an encrypted speech library in the cloud, through extracting uniform subband spectrum variance of the encrypted speech and constructing a hashing sequence to generate a hashing template of the cloud. In this way, a one-to-one correspondence between the encrypted speech and the hashing sequence is built. Secondly, the authentication digest of encrypted speech is extracted according to the inquiry result. Finally, the authentication digest and the hashing sequence in the cloud are matched by the Hamming distance algorithm. The experimental results demonstrate that the proposed method has great security and efficiency, and it can directly extract the authentication digest from encrypted speech. The authentication digest not only has good discrimination and robustness, but it accurately locates the tampered area for malicious substitution and mute attacks. [ABSTRACT FROM AUTHOR]

In the k -mappability problem, we are given a string x of length n and integers m and k , and we are asked to count, for each length- m factor y of x , the number of other factors of length m of x that are at Hamming distance at most k from y. We focus here on the version of the problem where k = 1. There exists an algorithm to solve this problem for k = 1 requiring time O (m n log ⁡ n / log ⁡ log ⁡ n) using space O (n). Here we present two new algorithms that require worst-case time O (m n) and O (n log ⁡ n log ⁡ log ⁡ n) , respectively, and space O (n) , thus greatly improving the previous result. Moreover, we present another algorithm that requires average-case time and space O (n) for integer alphabets of size σ if m = Ω (log σ ⁡ n). Notably, we show that this algorithm is generalizable for arbitrary k , requiring average-case time O (k n) and space O (n) if m = Ω (k log σ ⁡ n) , assuming that the letters are independent and uniformly distributed random variables. Finally, we provide an experimental evaluation of our average-case algorithm demonstrating its competitiveness to the state-of-the-art implementation. [ABSTRACT FROM AUTHOR]

We study the problem of similarity self-join and similarity join size estimation in a streaming setting where the goal is to estimate, in one scan of the input and with sublinear space in the input size, the number of record pairs that have a similarity within a given threshold. The problem has many applications in data cleaning and query plan generation, where the cost of a similarity join may be estimated before actually doing the join. On unary input where two records either match or don’t match, the problem becomes join and self-join size estimation for which one-pass algorithms are readily available. Our work addresses the problem for $d$ d -ary input, for $d \geq 1$ d ≥ 1 , where the degree of similarity can vary from 1 to $d$ d . We show that our proposed algorithm gives an accurate estimate and scales well with the input size. We provide error bounds and time and space costs, and conduct an extensive experimental evaluation of our algorithm, comparing its estimation accuracy to a few competitors, including some multi-pass algorithms. Our results show that given the same space, the proposed algorithm has an order of magnitude less error for a large range of similarity thresholds. [ABSTRACT FROM AUTHOR]

A border p of a string x is an enhanced cover of x if the number of positions of x that lie within some occurrence of p is the maximum among all borders of x. (String p is a border of x if p is both a proper prefix and a suffix of x.) In this paper, two more general notions based on enhanced covers are introduced: a k -approximate enhanced cover and a relaxed k -approximate enhanced cover, where a fixed maximum number of errors k under the Hamming distance is considered. The k -approximate enhanced cover of x is its border, and its k -approximate occurrences are also considered in the covered number of positions of x. The relaxed k -approximate enhanced cover of x is a factor of x and a k -approximate border of x. Algorithms that compute all the variations of k -approximate enhanced covers mentioned above are presented in this paper. [ABSTRACT FROM AUTHOR]

Given a set of n strings of length L and a radius d , the closest string problem (CSP for short) asks for a string t s o l that is within a Hamming distance of d to each of the given strings. It is known that the problem is NP-hard and its optimization version admits a polynomial time approximation scheme (PTAS). A number of parameterized algorithms have been then developed to solve the problem when d is small. Among them, the relatively new ones have not been implemented before and their performance in practice was unknown. In this study, we implement all of them by careful engineering. For those that have been implemented before, our implementation is much faster. For some of those that have not been implemented before, our experimental results show that there exist huge gaps between their theoretical and practical performances. We also design a new parameterized algorithm for the binary case of CSP. The algorithm is deterministic and runs in O (n 2 L + n 2 d ⋅ 6.16 d) time, while the previously best deterministic algorithm runs in O (n L + n d 3 ⋅ 6.731 d) time. [ABSTRACT FROM AUTHOR]

Given n vectors x 0 , x 1 , ... , x n − 1 in { 0 , 1 } m , how to find two vectors whose pairwise Hamming distance is minimum? This problem is known as the Closest Pair Problem. If these vectors are generated uniformly at random except two of them are correlated with Pearson-correlation coefficient ρ , then the problem is called the Light Bulb Problem. In this work, we propose a novel coding-based scheme for the Closest Pair Problem. We design both randomized and deterministic algorithms, which achieve the best-known running time when the length of input vectors m is small and the minimum distance is very small compared to m. Specifically, the running time of our randomized algorithm is O (n log 2 ⁡ n ⋅ 2 c m ⋅ poly (m)) and the running time of our deterministic algorithm is O (n log ⁡ n ⋅ 2 c ′ m ⋅ poly (m)) , where c and c ′ are constants depending only on the (relative) distance of the closest pair. When applied to the Light Bulb Problem, our result yields state-of-the-art deterministic running time when the Pearson-correlation coefficient ρ is very large. Specifically, when ρ ≥ 0.9933 , our deterministic algorithm runs faster than the previously best deterministic algorithm (Alman, SOSA 2019). [ABSTRACT FROM AUTHOR]

In fact, compression and computation are two sides of the same coin, as they exploit the same underlying structure both for storing and operating on data. The study in [[4]] establishes new upper bounds and a conditional lower bound on the indexed regular expression matching problem and [[5]] improves existing analyses on the approximation ratios for common grammar-based compressors. As the production of massive data has outpaced Moore's law in many scientific areas, the very notion of algorithms is transforming. [Extracted from the article]

Mutually uncorrelated (MU) codes are a class of codes in which no proper prefix of one codeword is a suffix of another codeword. These codes were originally studied for synchronization purposes and recently, Yazdi et al. showed their applicability to enable random access in DNA storage. In this paper,we follow the research of Yazdi et al. and study MU codes along with their extensions to correct errors and balanced codes. We first review a well-known construction of MU codes and study the asymptotic behavior of its cardinality. This task is accomplished by studying a special class of run-length limited codes that impose the longest run of zeros to be at most some function of the codewords length. We also present an efficient algorithm for this class of constrained codes and show how to use this analysis for MU codes. Next, we extend the results on the run-length limited codes in order to study $(d_{h},d_{m})$ -MU codes that impose a minimum Hamming distance of $d_{h}$ between different codewords and $d_{m}$ between prefixes and suffixes. In particular, we show an efficient construction of these codes with nearly optimal redundancy. We also provide similar results for the edit distance and balanced MU codes. Last, we draw connections to the problems of comma-free and prefix synchronized codes. [ABSTRACT FROM AUTHOR]

In this paper, a novel chaotic circuit with one memcapacitor is designed, which has abundant dynamic behaviors. As a potential application, combining the DNA binding mode and the characteristics of the chaotic system, a new image encryption scheme is proposed. Firstly, the original image is processed and generates a set of hash values by the SHA-3 algorithm. The generated hash value and original image are performed XOR operation. The hash values are processed to generate the initial value of the chaotic system by the Hamming distance. Furthermore, the elliptic curve with the hyperchaotic sequence is used to construct the Hill encryption matrix, and the plaintext image is permuted and encrypted. At last, the proposed chaotic system is used to scramble the image. The simulation results and theoretical analysis show that the chaotic system has abundant dynamic behaviors, and the proposed algorithm has a better anti-interference ability for image and information encryption. [ABSTRACT FROM AUTHOR]

This paper presents a novel star identification algorithm for a “lost-in-space” mode star tracker. The Spearman-correlation approach provides reliable recognition even when the captured images are swayed and biased from the onboard star pattern database. The hamming distance approach provides a shortlisted list of star IDs. Thus, the proposed combination of hamming distance and Spearman correlation provides a reliable and fast recognition. The achievable performance is evaluated by testing on simulated and real images. [ABSTRACT FROM AUTHOR]

List decoding of insertions and deletions in the Levenshtein metric is considered. The Levenshtein distance between two sequences is the minimum number of insertions and deletions needed to turn one of the sequences into the other. In this paper, a Johnson-like upper bound on the maximum list size when list decoding in the Levenshtein metric is derived. This bound depends only on the length and minimum Levenshtein distance of the code, the length of the received word, and the alphabet size. It shows that polynomial-time list decoding beyond half the Levenshtein distance is possible for many parameters. Further, we also prove a lower bound on list decoding of deletions with the well-known binary Varshamov–Tenengolts codes, which shows that the maximum list size grows exponentially with the number of deletions. Finally, an efficient list decoding algorithm for two insertions/deletions with VT codes is given. This decoder can be modified to a polynomial-time list decoder of any constant number of insertions/deletions. [ABSTRACT FROM AUTHOR]

This paper proposes new algorithms for fixed-length approximate string matching and approximate circular string matching under the Hamming distance. Fixed-length approximate string matching and approximate circular string matching are special cases of approximate string matching and have numerous direct applications in bioinformatics and text searching. Firstly, a counter-vector-mismatches (CVM) algorithm is proposed to solve fixed-length approximate string matching with k-mismatches. The development of CVM algorithm is based on the parallel summation of counters located in the same machine word. Secondly, a parallel counter-vector-mismatches (PCVM) algorithm is proposed to accelerate CVM algorithm in parallel. The PCVM algorithm is integrated into two-level parallelisms that exploit not only word-level parallelism but also data parallelism via parallel environments such as multi-core processors and graphics processing units (GPUs). In the particular case of adopting GPUs, a shared-mem parallel counter-vector-mismatches (PCVMsmem) scheme can be implemented from PCVM algorithm. The PCVMsmem scheme can exploit the memory model of GPUs to optimize performance of PCVM algorithm. Finally, this paper shows several methods to adopt CVM and PCVM algorithms in case the input pattern is in circular structure. In the experiments with real DNA packages, our proposed algorithms and scheme work greatly faster than previous bit-vector-mismatches and parallel bit-vector-mismatches algorithms. [ABSTRACT FROM AUTHOR]

Algebraic-geometric (AG) codes have good error-correction capability due to their generally large code word length. However, their decoding remains complex, preventing practical applications. Addressing the challenge, this paper proposes two interpolation-based low-complexity Chase (LCC) decoding algorithms for one of the most popular AG codes-Hermitian codes. By choosing $\eta $ unreliable symbols and realizing them with the two most likely decisions, $2^\eta $ decoding test-vectors can be formulated. The first LCC algorithm performs interpolation for the common elements of the test-vectors, producing an intermediate outcome that will be shared by the uncommon element interpolation. It eliminates the redundant computation for decoding each test-vector, resulting in a low-complexity. With an interpolation multiplicity of one, the decoding is further facilitated by removing the requirement of pre-calculating the Hermitian curve’s corresponding coefficients. The second LCC algorithm is an adaptive variant of the first algorithm, where the number of test-vectors is determined by the reliability of received information. When the channel condition improves, it can reduce the complexity without compromising the decoding performance. Simulation results show that the both LCC algorithms outperform a number of existing algebraic decoding algorithms for Hermitian codes. Finally, our complexity analysis will reveal the proposals’ low-complexity feature. [ABSTRACT FROM PUBLISHER]

A string T of length m is periodic in P of length p if P is a substring of T and T [ i ] = T [ i + p ] for all 0 ≤ i ≤ m − p − 1 and m ≥ 2 p . The shortest such prefix, P , is called the period of T (i.e., P = T [ 0 . . p − 1 ] ). In this paper we investigate the period recovery problem. Given a string S of length n , find the primitive period(s) P such that the distance between S and a string T that is periodic in P is below a threshold τ . We consider the period recovery problem over both the Hamming distance and the edit distance. For the Hamming distance case, we present an O ( n log ⁡ n ) -time algorithm, where τ is given as ⌊ n ( 2 + ϵ ) p ⌋ , for ϵ > 0 . For the edit distance case, τ = ⌊ n ( 3.75 + ϵ ) p ⌋ and ϵ > 0 , we provide an O ( n 4 / 3 ) -time algorithm. [ABSTRACT FROM AUTHOR]

The idea of the inverse optimization problem is to adjust the value of the parameters such that the observed feasible solution becomes optimal. The modification cost can be measured by different norms, such as l 1 , l 2 , l ∞ norms and the Hamming distance, and the goal is to adjust the parameters as little as possible. In this paper, we consider the inverse minimum flow problem under the weighted sum-type Hamming distance, where the lower and upper bounds for the arcs should be changed as little as possible under the weighted sum-type Hamming distance such that a given feasible flow becomes a minimum flow. Two models are considered: the unbounded case and the general bounded case. We present their respective combinatorial algorithms that both run in O ( n m ) time in terms of the minimum cut method. Computational examples are presented to illustrate our algorithms. [ABSTRACT FROM AUTHOR]

Accurate and fast target image recognition is an important function of applications such as remote sensing imaging and medical imaging. However, an operator such as speeded up robust feature (SURF) cannot be accurately matched in the recognition process of a target image. This led us to propose the use of a method capable of matching identification, i.e. binary robust invariant scalable keypoints (BRISK) operators, in combination with SURF operators. The proposed algorithm combines the accuracy of SURF operators and the rapidity of BRISK operators to obtain a quick and accurate way of matching. The initial matching of image feature extraction for targets is performed using the SURF-BRISK algorithm, and similarity measurements of feature matching are performed for the feature points of initial matching using the Hamming distance. Then, secondary fine matching is performed using the M-estimator Sample and Consensus (MSAC) algorithm to eliminate mismatched point pairs in order to achieve recognition of target images. Then, the three-dimensional coordinates of the work piece are obtained by using a binocular stereo vision system to provide location coordinates for the robots to grasp the work pieces accurately. In the experiment, stereo vision matching is conducted for targets obtained using the SURF-BRISK algorithm, and the location coordinates of targets are passed to the robot controller. The experimental results show that if the special geometric distortion is neglected, this method can be adapted for accurate positioning of the target; hence, it can identify the target in complex environments, access the location coordinates of the target, and achieve accurate robotic grasping of the work piece in real time. [ABSTRACT FROM AUTHOR]

Motif finding is an important and a challenging problem in many biological applications such as discovering promoters, enhancers, locus control regions, transcription factors, and more. The ( l, d)-planted motif search, PMS, is one of several variations of the problem. In this problem, there are n given sequences over alphabets of size , each of length m, and two given integers l and d. The problem is to find a motif m of length l, where in each sequence there is at least an l-mer at a Hamming distance of of m. In this article, we propose ET-Motif, an algorithm that can solve the PMS problem in time and space. The time bound can be further reduced by a factor of m with space. In case the suffix tree that is built for the input sequences is balanced, the problem can be solved in time and space. Similarly, the time bound can be reduced by a factor of m using space. Moreover, the variations of the problem, namely the edit distance PMS and edited PMS (Quorum), can be solved using ET-Motif with simple modifications but upper bands of space and time. For edit distance PMS, the time and space bounds will be increased by , while for edited PMS the increase will be of in the time bound. [ABSTRACT FROM AUTHOR]

Symbol-pair read channels, in which the outputs of the read process are pairs of consecutive symbols, were recently studied by Cassuto and Blaum. This new paradigm is motivated by the limitations of the reading process in high density data storage systems. They studied error correction in this new paradigm, specifically, the relationship between the minimum Hamming distance of an error correcting code and the minimum pair distance, which is the minimum Hamming distance between symbol-pair vectors derived from codewords of the code. It was proved that for a linear cyclic code with minimum Hamming distance dH , the corresponding minimum pair distance is at least dH+3 . In this paper, we show that, for a given linear cyclic code with a minimum Hamming distance dH , the minimum pair distance is at least dH +\left \lceil{ {dH/{2}}}\right \rceil . We then describe a decoding algorithm, based upon a bounded distance decoder for the cyclic code, whose symbol-pair error correcting capabilities reflect the larger minimum pair distance. Finally, we consider the case where the read channel output is a larger number, $b \geqslant 3$ , of consecutive symbols, and we provide extensions of several concepts, results, and code constructions to this setting. [ABSTRACT FROM AUTHOR]

A stochastic algorithm for obtaining feasible initial populations to the Vehicle Routing Problem with Time Windows is presented. The theoretical formulation for the Vehicle Routing Problem with Time Windows is explained. The proposed method is primarily divided into a clustering algorithm and a two-phase algorithm. The first step is the application of a modified k-means clustering algorithm which is proposed in this paper. The two-phase algorithm evaluates a partial solution to transform it into a feasible individual. The two-phase algorithm consists of a hybridization of four kinds of insertions which interact randomly to obtain feasible individuals. It has been proven that different kinds of insertions impact the diversity among individuals in initial populations, which is crucial for population-based algorithm behavior. A modification to the Hamming distance method is applied to the populations generated for the Vehicle Routing Problem with Time Windows to evaluate their diversity. Experimental tests were performed based on the Solomon benchmarking. Experimental results show that the proposed method facilitates generation of highly diverse populations, which vary according to the type and distribution of the instances. [ABSTRACT FROM AUTHOR]

Approximate pattern matching is a fundamental problem in the bioinformatics and information retrieval applications. The problem involves different matching relations such as Hamming distance, edit distances, and the wildcards matching problem. The input is usually a text of length n over a fixed alphabet of length Σ, a pattern of length m, and an integer k. The output is to find all positions that have ≤ k Hamming distance, edit distance, or wildcards matching with P. Many algorithms and indexes have been proposed to solve the problems more efficiently, but due to the space and time complexities of the problems, most tools adopted heuristics approaches based on, for instance, suffix tree, suffix array, or Burrows Wheeler Transform to reach practical implementations. Error Tree is a novel tree structure that is mainly oriented to solve the approximate pattern matching problems, using less space and faster computation time. The algorithm proposes for Hamming distance and wildcards matching a tree structure that needs words and takes in the average case) of query time for any online/offline pattern, where occ is the number of outputs. In addition, a tree structure of words and in the average case) query time for edit distance for any online/offline pattern. [ABSTRACT FROM AUTHOR]

The Closest String problem asks to find a string s which is not too far from each string in a set of m input strings, where the distance is taken as the Hamming distance. This well-studied problem has various applications in computational biology and drug design. In this paper, we introduce a new variant of Closest String where the input strings can contain wildcards that can match any letter in the alphabet, and the goal is to find a solution string without wildcards. We call this problem the Closest String with Wildcards problem, and we analyze it in the framework of parameterized complexity. Our study determines for each natural parameterization whether this parameterization yields a fixed-parameter algorithm, or whether such an algorithm is highly unlikely to exist. [ABSTRACT FROM AUTHOR]

The uniform experimental design (UD), a major kind of space-filling design, is widely used in applications. The majority of UD tables (UDs) with good uniformity are generated under the centralized L 2 -discrepancy (CD) and the wrap-around L 2 -discrepancy (WD). Recently, the mixture L 2 -discrepancy (MD) is proposed and shown to be more reasonable than CD and WD in terms of uniformity. In this paper we review lower bounds for MD of two-level designs from a different point of view and provide a new lower bound. Following the same idea we obtain a lower bound for MD of three-level designs. Moreover, we construct UDs under the measurement of MD by the threshold accepting (TA) algorithm, and finally we attach two new UD tables with good properties derived from TA under the measurement of MD. [ABSTRACT FROM AUTHOR]

Consider two remote nodes having binary sequences $X$ and Y$ , respectively. Y$ is an edited version of , where the editing involves random deletions, insertions, and substitutions, possibly in bursts. The goal is for the node with Y$ to reconstruct X$ with minimal exchange of information over a noiseless link. The communication is measured in terms of both the total number of bits exchanged and the number of interactive rounds of communication. This paper focuses on the setting where the number of edits is , where $n$ is the length of $X$ . We first consider the case where the edits are a mixture of insertions and deletions (indels), and propose an interactive synchronization algorithm with near-optimal communication rate and average computational complexity of $O(n)$ arithmetic operations. The algorithm uses interaction to efficiently split the source sequence into substrings containing exactly one deletion or insertion. Each of these substrings is then synchronized using an optimal one-way algorithm based on the single-deletion correcting channel codes of Varshamov and Tenengolts. We then build on this synchronization algorithm in three different ways. First, it is modified to work with a single round of interaction. The reduction in the number of rounds comes at the expense of higher communication, which is quantified. Next, we present an extension to the practically important case where the insertions and deletions may occur in (potentially large) bursts. Finally, we show how to synchronize the sources to within a target Hamming distance. This feature can be used to differentiate between substitution and indel edits. In addition to theoretical performance bounds, we provide several validating simulation results for the proposed algorithms. [ABSTRACT FROM PUBLISHER]

We study the power of Arthur–Merlin probabilistic proof systems in the data stream model. We show a canonical AM streaming algorithm for a class of data stream problems. The algorithm offers a tradeoff between the length of the proof and the space complexity that is needed to verify it. As an application, we give an AM streaming algorithm for the Distinct Elements problem. Given a data stream of length m over alphabet of size n , the algorithm uses O ˜ ( s ) space and a proof of size O ˜ ( w ) , for every s , w such that s ⋅ w ≥ n (where O ˜ hides a polylog ( m , n ) factor). We also prove a lower bound, showing that every MA streaming algorithm for the Distinct Elements problem that uses s bits of space and a proof of size w , satisfies s ⋅ w = Ω ( n ) . Furthermore, the lower bound also holds for approximating the number of distinct elements within a multiplicative factor of 1 ± 1 / n . As a part of the proof of the lower bound for the Distinct Elements problem, we show a new lower bound of Ω ( n ) on the MA communication complexity of the Gap Hamming Distance problem, and prove its tightness. [ABSTRACT FROM AUTHOR]

In this paper, we consider several variants of the pattern matching with mismatches problem. In particular, given a text T = t1t2 . . . tn and a pattern P = p1p2 . . . pm, we investigate the following problems: (1) pattern matching with mismatches: for every i; 1 ≤ i ≤ n - m + 1 output, the distance between P and titi+1 . . . ti+m-1 and (2) pattern matching with k mismatches: output those positions i where the distance between P and tiiti+1 . . . ti+m-1 is less than a given threshold k. The distance metric used is the Hamming distance. We present some novel algorithms and techniques for solving these problems. We offer deterministic, randomized and approximation algorithms. We consider variants of these problems where there could be wild cards in either the text or the pattern or both. We also present an experimental evaluation of these algorithms. The source code is available at http://www.engr.uconn.edu/∼man09004/kmis.zip. [ABSTRACT FROM AUTHOR]