Fast Algorithm Research Articles

A Simple and Fast Algorithm for Generating Correlation Matrices with a Known Average Correlation Coefficient

This article describes a simple and fast algorithm for generating correlation matrices ( R ) with a known average correlation. The algorithm should be useful for researchers desiring plausible R matrices for substantive domains in which average correlations are known (at least approximately). The method is non-iterative and it can solve relatively large problems (e.g., generate a 500 × 500 R matrix) in less than a second on a personal computer. It also has didactic value for introducing students to the convex set of feasible R matrices of a fixed dimension. This Euclidean body is called an elliptope. The proposed method exploits the geometry of elliptopes to efficiently generate realistic R matrices with a desired average correlation coefficient. R code for implementing the algorithm (and for reproducing all of the results of this article) is reported in an online supplement.

Fast, high-order numerical evaluation of volume potentials via polynomial density interpolation

This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poisson and Helmholtz equations in two dimensions. Following the ideas of the density interpolation method for boundary integral operators, the proposed methodology leverages Green's third identity and a local polynomial interpolant of the density function to recast the volume potential as a sum of single- and double-layer potentials and a volume integral with a regularized (bounded or smoother) integrand. The layer potentials can be accurately and efficiently evaluated everywhere in the plane by means of existing methods (e.g. the density interpolation method), while the regularized volume integral can be accurately evaluated by applying elementary quadrature rules. Compared to straightforwardly computing corrections for every singular and nearly-singular volume target, the method significantly reduces the amount of required specialized quadrature by pushing all singular and near-singular corrections to near-singular layer-potential evaluations at target points in a small neighborhood of the domain boundary. Error estimates for the regularization and quadrature approximations are provided. The method is compatible with well-established fast algorithms, being both efficient not only in the online phase but also to set-up. Numerical examples demonstrate the high-order accuracy and efficiency of the proposed methodology; applications to inhomogeneous scattering are presented.

Fast algorithms for the solution of perturbed symmetric Toeplitz linear system and its applications

Fast algorithms for the solution of perturbed symmetric Toeplitz linear system and its applications

Laminography as a tool for imaging large-size samples with high resolution.

Despite the increased brilliance of the new generation synchrotron sources, there is still a challenge with high-resolution scanning of very thick and absorbing samples, such as a whole mouse brain stained with heavy elements, and, extending further, brains of primates. Samples are typically cut into smaller parts, to ensure a sufficient X-ray transmission, and scanned separately. Compared with the standard tomography setup where the sample would be cut into many pillars, the laminographic geometry operates with slab-shaped sections significantly reducing the number of sample parts to be prepared, the cutting damage and data stitching problems. In this work, a laminography pipeline for imaging large samples (>1 cm) at micrometre resolution is presented. The implementation includes a low-cost instrument setup installed at the 2-BM micro-CT beamline of the Advanced Photon Source. Additionally, sample mounting, scanning techniques, data stitching procedures, a fast reconstruction algorithm with low computational complexity, and accelerated reconstruction on multi-GPU systems for processing large-scale datasets are presented. The applicability of the whole laminography pipeline was demonstrated by imaging four sequential slabs throughout an entire mouse brain sample stained with osmium, in total generating approximately 12 TB of raw data for reconstruction.

Design of Fast Mining Algorithm for Educational Sport Course Data Based on Cluster Analysis

In this age of big data, education researchers are reconceptualizing and re-evaluating the value of education data. Therefore, we need to use educational data mining methods for data analysis to better guide teaching. The informatization level of colleges and universities is improving year by year, and the entire training data of students from enrollment to graduation is stored. These datasets are collected, stored, and kept by different departments, contain a large amount of regular and relevant information, and truly record the growth footprint of students. Traditional educational decision-making has not yet fully explored and used the valuable information hidden in data resources. Although some scholars have carried out research related to campus data mining at this stage, there are still many problems that have not yet been solved in the application of decision-making in colleges and universities. This paper is based on the idea of data-driven decision-making, combined with the data characteristics of campus big data, and establishes a model solution for student behavior analysis and behavior prediction by applying multiple machine learning algorithms. On the basis of the analysis of students’ academic behavior performance in the context of multi-category educational data, we proposed a cluster analysis framework for processing multi-type campus big data, and described the group characteristics of the clustering results. By introducing the K-prototype algorithm, we effectively solved the multi-category problem where traditional clustering algorithms (such as K-Means, etc.) cannot adapt to the attributes of educational data. The research results show that innovative educational decision-making models and methods are based on the idea of “data-prediction-decision”, which promotes the application research of big data science in the area of education.

Fast computation of General SimRank on heterogeneous information network

Similarity computation is a fundamental aspect of information network analysis, underpinning many research tasks including information retrieval, clustering, and recommendation systems. General SimRank (GSR), an extension of the well-known SimRank algorithm, effectively computes link-based global similarities incorporating semantic logic within heterogeneous information networks (HINs). However, GSR inherits the recursive nature of SimRank, making it computationally expensive to achieve convergence through iterative processes. While numerous rapid computation methods exist for SimRank, their direct application to GSR is impeded by differences in their underlying equations. To accelerate GSR computation, we introduce a novel approach based on linear systems. Specifically, we transform the pairwise surfer model of GSR on HINs into a new random walk model on a node-pair graph, establishing an equivalent linear system for GSR. We then develop a fast algorithm utilizing the local push technique to compute all-pair GSR scores with guaranteed accuracy. Additionally, we adapt the local push method for dynamic HINs and introduce a corresponding incremental algorithm. Experimental results on various real datasets demonstrate that our algorithms significantly outperform the traditional power method in both static and dynamic HIN contexts.

Birational reparameterizations of surfaces

Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational parameterization with empty base locus, and the input parameterization is transversal, the degree of the solution is determined in advance and the dimension of the space of solutions is reduced. As a consequence, for these cases, we present a second faster algorithm.

A fast bootstrap algorithm for causal inference with large data.

Estimating causal effects from large experimental and observational data has become increasingly prevalent in both industry and research. The bootstrap is an intuitive and powerful technique used to construct standard errors and confidence intervals of estimators. Its application however can be prohibitively demanding in settings involving large data. In addition, modern causal inference estimators based on machine learning and optimization techniques exacerbate the computational burden of the bootstrap. The bag of little bootstraps has been proposed in non-causal settings for large data but has not yet been applied to evaluate the properties of estimators of causal effects. In this article, we introduce a new bootstrap algorithm called causal bag of little bootstraps for causal inference with large data. The new algorithm significantly improves the computational efficiency of the traditional bootstrap while providing consistent estimates and desirable confidence interval coverage. We describe its properties, provide practical considerations, and evaluate the performance of the proposed algorithm in terms of bias, coverage of the true 95% confidence intervals, and computational time in a simulation study. We apply it in the evaluation of the effect of hormone therapy on the average time to coronary heart disease using a large observational data set from the Women's Health Initiative.

Mobile LiDAR-based Real-time Identification of Transmission Lines

Abstract. This paper proposes a method for identifying 3D point cloud of transmission line acquired by light detection and ranging (LiDAR) real-time mobile scanning. Since the single frame of point cloud obtained by LiDAR is sparse, the method employs a sliding spatial window strategy with Kalman filtering for dynamic point cloud registration. Then, a 3D point cloud deep learning neural network that utilizes uniform sampling and local feature aggregation (LFA) is designed specifically for transmission line objects. The network handles the problem of long-span objects and a large amount of point cloud. Finally, the instantiated transmission line objects are extracted from the top-down projection of the semantically segmented 3D point cloud by fast Euclidean clustering algorithm. Experiments demonstrate that the method achieves a classification accuracy of 94.7% and a mean intersection over union of 81.6% on 3D point cloud datasets of transmission line obtained from LiDAR mobile scanning, validating its ability to achieve real-time identification and distance measurement of transmission line objects.

Balancing the cardinality of clusters with a distance constraint: a fast algorithm

AbstractLogistics companies partition the customers they serve into delivery zones as a tactical decision and manage the customers assigned to each zone as a cluster for the purpose of routing, workload allocation, etc. Frequently, this partition is made in accordance with customers’ geographical location, which can result in very unbalanced clusters in terms of the number of customers they include. In addition, in the day-to-day operations, not necessarily all customers need to be served every day so, even if the clusters originally created are balanced, daily needs may lead to unbalanced clusters. Given an a priori assignment of customers to clusters, improving the balance between clusters in advance of workload management is therefore a key issue. This paper addresses the problem of balancing clusters, when there is a distance constraint that prevents reassigning customers to clusters far away from their original pre-assignment. This problem is formulated as a lexicographic biobjective optimization model. The highest priority objective function minimizes the variance of the number of customers in the clusters. The second ranked objective function minimizes the total distance resulting from all reassignments. A fast and effective heuristic algorithm is developed, based on exploring customer reassignments, either by comparing clusters two by two or by extending the search to allow for sequential customer swaps among clusters. Both the quality of the solution and the computational time required encourage the use of this algorithm by logistics companies to balance clusters in real scenarios.

Large-scale DSM registration via motion averaging

Abstract. Generating wide-area digital surface models (DSMs) requires registering a large number of individual, and partially overlapped DSMs. This presents a challenging problem for a typical registration algorithm, since when a large number of observations from these multiple DSMs are considered, it may easily cause memory overflow. Sequential registration algorithms, although can significantly reduce the computation, are especially vulnerable for small overlapped pairs, leading to a large error accumulation. In this work, we propose a novel solution that builds the DSM registration task as a motion averaging problem: pair-wise DSMs are registered to build a scene graph, with edges representing relative poses between DSMs. Specifically, based on the grid structure of the large DSM, the pair-wise registration is performed using a novel nearest neighbor search method. We show that the scene graph can be optimized via an extremely fast motion average algorithm with O(N) complexity (N refers to the number of images). Evaluation of high-resolution satellite-derived DSM demonstrates significant improvement in computation and accuracy.

A hybrid metaheuristic algorithm for scheduling iron ore reclaiming in ports

ABSTRACT This work deals with a scheduling problem of reclaimers. This problem involves a set of ships to be loaded with predefined stockpiles. These stockpiles are unloaded into ship holds, and each hold must store a predefined product and quantity of iron ore. Stockpiles are stored in storage yards, which have reclaimers to reclaim iron ore from stockpiles and send it to berthed ships. The objective is to schedule the operations of reclaimers to minimize the sum of ships' berthing times. A hybrid algorithm, combining the multi-start, GRASP and variable neighbourhood descent procedures, is proposed to treat instances of any scale of the problem. It was tested in real instances, and its results were compared with the hybrid simulated annealing algorithm from the literature and a fast simulation algorithm that emulates operators' decision-making. The proposed algorithm was the best in all instances, and statistical tests proved its superiority

High order compact augmented methods for Stokes equations with different boundary conditions

This paper is devoted to fourth order compact schemes and fast algorithms for solving stationary Stokes equations with different boundary conditions numerically. One of the main ideas is to decouple the Stokes equations into three Poisson equations for the pressure and the velocity via the pressure Poisson equation (PPE). The augmented strategy is utilized to provide numerical boundary conditions for the pressure. Different velocity boundary conditions require different interpolation strategies for the augmented methods. The augmented variable is solved by the GMRES method. A new simple and efficient preconditioning strategy has also been developed to accelerate the convergence of the GMRES iteration. Numerical examples presented in this paper confirmed the designed convergence order and the efficiency of the new methods.

A new fast four-point rainflow cycle counting algorithm by employing a new loop iteration mode for fatigue life estimation

Purpose In order to improve the computation efficiency of the four-point rainflow algorithm, a new fast four-point rainflow cycle counting algorithm (FFRA) using a novel loop iteration mode is proposed.Design/methodology/approach In this new algorithm, the loop iteration mode is simplified by reducing the number of iterations, tests and deletions. The high efficiency of the new algorithm makes it a preferable candidate in fatigue life online estimation of structural health monitoring systems.Findings The extensive simulation results show that the extracted cycles by the new FFRA are the same as those by the four-point rainflow cycle counting algorithm (FRA) and the three-point rainflow cycle counting algorithm (TRA). Especially, the simulation results indicate that the computation efficiency of the FFRA has improved an average of 12.4 times compared to the FRA and an average of 8.9 times compared to the TRA. Moreover, the equivalence of cycle extraction results between the FFRA and the FRA is proved mathematically by utilizing some fundamental properties of the rainflow algorithm. Theoretical proof of the efficiency improvement of the FFRA in comparison to the FRA is also given.Originality/value This merit makes the FFRA preferable in online monitoring systems of structures where fatigue life estimation needs to be accomplished online based on massive measured data. It is noticeable that the high efficiency of the FFRA attributed to the simple loop iteration, which provides beneficial guidance to improve the efficiency of existing algorithms.

Bilateral Half-Box Image Filtering

Because edge-aware filtering has been widely used for image-based automation technologies, developing a practical, fast algorithm for its use is important. This letter proposes a simple and fast computational method for edge-aware image filtering based on bilateral half-box regions. Our filter consists of a weighted average of only eight color sums within each half-box region adjacent to a given pixel, where the tonal weights are similar to those obtained with bilateral filtering. The eight sums are efficiently obtained by a single fast box filter using the relative coordinate relationship between the pixel and each half-box center. We examined the performance of our filter based on comparisons with conventional methods.

Research on Urban Architecture Design under the Concept of Smart City

After the digital city and smart city concepts, the latest proposed smart city concept is a general summary of the advanced form of urban information development, which plays an important role in the economic transformation of cities, social governance, improvement of residents' quality of life and energy conservation and environmental protection. The smart city puts forward new requirements for the architectural design of the city, and how to reasonably use the smart city concept in the architectural design is still a major issue for architects and professionals to think about. To this end, this paper proposes a state tracking based full working condition modeling method for nonlinear industrial systems. For the problem that the amount of historical data is too large and it is difficult to screen the modeling data, a sliding window is designed to screen the steady-state data, and a fast recursive algorithm of standard deviation in the window is derived; the influence mechanism of unknown disturbances on the system is analyzed, and the data modeling by dynamic regression to the steady state is selected, and a data-driven modeling algorithm that can eliminate the influence of disturbances is proposed; the model information contained in the process industrial big data is used to apply the higher order function to fit each A linear variable parameter transfer function model based on the characteristic parameters is proposed. The identification of an industrial process is shown to be effective. The main points of urban architectural design should be noted under the concept of smart city from four aspects: safety, diversity, environmental protection and emotionality.

Faster space-efficient STR-IC-LCS computation

One of the most fundamental method for comparing two given strings A and B is the longest common subsequence (LCS), where the task is to find (the length) of an LCS of A and B. In this paper, we deal with the STR-IC-LCS1 problem which is one of the constrained LCS problems proposed by Chen and Chao [J. Comb. Optim, 2011]. A string Z is said to be an STR-IC-LCS of three given strings A, B, and P, if Z is a longest string satisfying that (1) Z includes P as a substring and (2) Z is a common subsequence of A and B. We present three efficient algorithms for this problem: First, we begin with a space-efficient solution which computes the length of an STR-IC-LCS in O(n2) time and O((ℓ+1)(n−ℓ+1)) space, where ℓ is the length of an LCS of A and B of length n. When ℓ=O(1) or n−ℓ=O(1), then this algorithm uses only linear O(n) space. Second, we present a faster algorithm that works in O(nr/log⁡r+n(n−ℓ+1)) time, where r is the length of P, while retaining the O((ℓ+1)(n−ℓ+1)) space efficiency. Third, we give an alternative algorithm that runs in O(nr/log⁡r+n(n−ℓ′+1)) time with O((ℓ′+1)(n−ℓ′+1)) space, where ℓ′ denotes the STR-IC-LCS length for input strings A, B, and P.

FastCCLasso: a fast and efficient algorithm for estimating correlation matrix from compositional data.

The composition and structure of microbial communities on the body surface are closely related to human health. The interaction relationship among microbes can help us understand the formation of the microecological environment and the biological mechanism by which microorganisms influence host health. With the help of high-throughput sequencing technologies, microbial abundances in a natural environment can be directly measured without the isolation of microorganisms in culture. Sequencing experiments in microbiome studies can measure the relative abundance of microbes, which is called compositional data. Although there are already many methods for correlation analysis for compositional data, the computation time or accuracy still needs to be improved for current microbiome studies. We develop a fast and efficient algorithm, called fastCCLasso, based on a penalized weighted least squares for inferring the correlation structure of microbes from compositional data in microbiome studies. We perform a large number of numerical experiments and the simulation results show that fastCCLasso outperforms its competitors in edge detection for inferring the correlation network. We also apply fastCCLasso for estimating microbial networks in microbiome studies and fastCCLasso provides a conservative network with comparable false discovery counts that are derived from shuffled data. FastCCLasso is open source and freely available from https://github.com/ShenZhang-Statistics/fastCCLasso under GNU LGPL v3.

Fast Coding Unit Partitioning Algorithm for Video Coding Standard Based on Block Segmentation and Block Connection Structure and CNN

The recently introduced Video Coding Standard, VVC, presents a novel Quadtree plus Nested Multi-Type Tree (QTMTT) block structure. This structure enables a more flexible block partition and demonstrates enhanced compression performance compared to its predecessor, HEVC. However, The introduction of the new structure has led to a more complex partition search process, resulting in a considerable increase in time complexity. The QTMTT structure yields diverse Coding Unit (CU) block sizes, posing challenges for CNN model inference. In this study, we propose a representation structure termed Block Segmentation and Block Connection (BSC), rooted in texture features. This ensures that partial CU blocks are uniformly represented in size. To address different-sized CUs, various levels of CNN models are designed for prediction. Moreover, we introduce a post-processing method and a multi-thresholding scheme to further mitigate errors introduced by CNNs. This allows for flexible and adjustable acceleration, achieving a trade-off between coding time complexity and performance. Experimental results indicate that, in comparison to VTM-10.0, our “Fast” scheme reduces the average complexity by 57.14% with a 1.86% increase in BDBR. Meanwhile, the “Moderate” scheme reduces average complexity by 50.14% with only a 1.39% increase in BDBR.

2772: Fast and accurate dose calculation algorithm based on multi-level U-Net for IMRT

2772: Fast and accurate dose calculation algorithm based on multi-level U-Net for IMRT