Sorting Algorithm Research Articles

PARALLEL BUCKET-SORT ALGORITHM ON OPTICAL CHAINED-CUBIC TREE INTERCONNECTION NETWORK

The performance of sorting algorithms has a great impact on many computationally intensive applications. Researchers worked on parallelizing many sorting algorithms on various interconnection networks to improve their sequential counterpart performance. One of these interconnection networks is the optical chained-cubic tree (OCCT). In this paper, a parallel bucket sort (PBS) algorithm is presented and applied to the OCCT interconnection network. This PBS algorithm is evaluated analytically and by simulation in terms of various performance metrics including parallel runtime, computation time, communication time, concatenation time, speedup, and efficiency, for a different number of processors, dataset sizes, and data distributions including random and descending. Simulation results show that the highest obtained speedup is approximately 912x on OCCT using 1020 processors, which means the parallel runtime of the PBS on 1020 processors is 912 times faster than the sequential runtime of BS on a single processor.

Sorting Visualizer: A Visual Journey Through Sorting Algorithms

This paper, which is based on the importance of sorting algorithms, will carefully compare the features of various algorithms, beginning with their work effectiveness, algorithm execution, introductory concepts, sorting styles, and other aspects, and make conclusions in order to create more effective sorting algorithms. Searching techniques and sorting algorithms are not the same. Sorting is placing the provided list in a predetermined order, which can be either ascending or descending, whereas searching is predicated on the possibility of finding a specific item in the list. Only a section of the data is sorted, and the piece of data that's actually used to establish the sorted order is the key. The maturity of this data is being compared. Depending on the kind of data structure, there are several algorithms for doing the same set of duties and other conditioning, and each has pros and cons of its own. Numerous sorting algorithms have been analysed grounded on space and time complexity. The aim of this relative study is to identify the most effective sorting algorithms or styles. This relative study grounded on the same analysis allows the user to select the applicable sorting algorithm for the given situation.

УДОСКОНАЛЕНА МОДЕЛЬ ПАРАЛЕЛЬНОГО АЛГОРИТМУ СОРТУВАННЯ З ФОРМУВАННЯМ РАНГІВ

The model of parallel sorting of a number array with ranking based on the simultaneous application of high-speed decrement/increment operations according to the array of numbers and the array of their ranks is improved. Acceleration of the proposed algorithm is achieved by fixing the result of zeroing (n -1) elements of the number array instead of its complete zeroing. The description of the algorithm of parallel sorting with the formation of ranks in a compact form using the basis of Glushkov’s system of algorithmic algebras (SAA) is given. Keywords: system of algorithmic algebras, parallel sorting, mask, rank, decrement/increment.

Stack sort: a new approach with sorting network and a buffer

Knuth introduced the problem of stack sorting. Stack sorting was implemented by t stacks in series. In this paper, we propose a new dimension to stack sorting problem by introducing a stack with sorting network and a petty buffer. Instead of using t stacks in series, it helps to improve the performance by avoiding shuffles the stack. The basic idea behind in this paper is to perform a stack sorting with a single stack, and to achieve greater performance. In this novel approach, 2 bit buffer is compared to stack and insert the element into stack in order to avoid multiple stack. The result shows the time complexity of the proposed algorithm is O (n)

Comparative Analysis of Sorting and Searching Algorithms

Comparative Analysis of Sorting and Searching Algorithms

Advanced Active Player Tracking System in Handball Videos Using Multi-Deep Sort Algorithm with GAN Approach

Advanced Active Player Tracking System in Handball Videos Using Multi-Deep Sort Algorithm with GAN Approach

Blockchain event ordering algorithm based on high-dimensional multi-objective differential evolution

Abstract Since the birth of Bitcoin, blockchain technology has been widely used in many fields, such as finance, supply chain management, smart contracts, etc.and has been highly valued for its decentralized and tamper-proof characteristics. With the expansion of application scenarios, blockchain faces inefficient data processing challenges, particularly in event sequencing and processing. Developing efficient event sequencing algorithms is a research priority to enhance the performance of blockchain systems. This study addresses the efficiency problem in blockchain event sequencing by introducing a high-dimensional multi-objective differential evolution strategy to improve blockchain technology’s performance in various fields. This paper uses the NSGA-III-WA algorithm to efficiently sort blockchain events by combining differential evolution strategies. Compared to the traditional sorting algorithm, this algorithm reduces latency by 30% and improves memory usage by about 20% when dealing with events of the same size, ensuring sorting accuracy. By optimizing the weight vector adjustment strategy, the convergence speed and distribution uniformity of the algorithm and the solution can be optimized. In this paper, the algorithm can effectively improve the efficiency and performance of blockchain event processing, which is critical in optimizing blockchain systems.

Advanced Model of Parallel Sorting Algorithm with Ranking

Advanced Model of Parallel Sorting Algorithm with Ranking

Matrix Reordering for Noisy Disordered Matrices: Optimality and Computationally Efficient Algorithms.

Motivated by applications in single-cell biology and metagenomics, we investigate the problem of matrix reordering based on a noisy disordered monotone Toeplitz matrix model. We establish the fundamental statistical limit for this problem in a decision-theoretic framework and demonstrate that a constrained least squares estimator achieves the optimal rate. However, due to its computational complexity, we analyze a popular polynomial-time algorithm, spectral seriation, and show that it is suboptimal. To address this, we propose a novel polynomial-time adaptive sorting algorithm with guaranteed performance improvement. Simulations and analyses of two real single-cell RNA sequencing datasets demonstrate the superiority of our algorithm over existing methods.

Correlation Analysis of International Student Exchange and the Enhancement of China’s International Cultural Communication Power Based on the Subsumption Sorting Algorithm

Abstract International students are a bridge between Chinese and foreign cultures, but they still face multiple dilemmas in Chinese cultural communication due to different cultural backgrounds and values. In this paper, we utilize the subsumption sorting algorithm to sort the amount of cultural communication of international students’ exchanges, which is dynamically switched by a combination of two methods: back-block forward interpolation and header exchange. The D-S monopolistic competition model is used to construct the theoretical model of international student exchange that affects China’s international cultural communication power. The CES utility function is used to construct China’s international cultural communication network, which calculates the total amount of communication culture of cross-cultural exchanges between international students. In the end, an analysis of 85 international student samples revealed a correlation between international student exchanges and China’s international cultural communication. The results show that the correlation coefficient between international student exchanges and China’s international cultural communication is 0.305 p > 0.05, indicating that international student exchanges have a positive promotion effect on China’s international cultural communication. This study examines the general law of international cultural communication, which is crucial in promoting Chinese culture worldwide.

Severe Convective Storms in Limited Instability Organized by Pattern and Distribution

Abstract Severe convection occurring in high-shear, low-CAPE (HSLC) environments is a common cool-season threat in the southeastern United States. Previous studies of HSLC convection document the increased operational challenges that these environments present compared to their high-CAPE counterparts, corresponding to higher false-alarm ratios and lower probability of detection for severe watches and warnings. These environments can exhibit rapid destabilization in the hours prior to convection, sometimes associated with the release of potential instability. Here, we use self-organizing maps (SOMs) to objectively identify environmental patterns accompanying HSLC cool-season severe events and associate them with variations in severe weather frequency and distribution. Large-scale patterns exhibit modest variation within the HSLC subclass, featuring strong surface cyclones accompanied by vigorous upper-tropospheric troughs and northward-extending regions of instability, consistent with prior studies. In most patterns, severe weather occurs immediately ahead of a cold front. Other convective ingredients, such as lower-tropospheric vertical wind shear, near-surface equivalent potential temperature (θe) advection, and the release of potential instability, varied more significantly across patterns. No single variable used to train SOMs consistently demonstrated differences in the distribution of severe weather occurrence across patterns. Comparison of SOMs based on upper and lower quartiles of severe occurrence demonstrated that the release of potential instability was most consistently associated with higher-impact events in comparison to other convective ingredients. Overall, we find that previously developed HSLC composite parameters reasonably identify high-impact HSLC events. Significance Statement Even when atmospheric instability is not optimal for severe convective storms, in some situations they can still occur, presenting increased challenges to forecasters. These marginal environments may occur at night or during the cool season, when people are less attuned to severe weather threats. Here, we use a sorting algorithm to classify different weather patterns accompanying such storms, and we distinguish which specific patterns and weather system features are most strongly associated with severe storms. Our goals are to increase situational awareness for forecasters and to improve understanding of the processes leading to severe convection in marginal environments.

Analysis and Comparison of Exchange Sorting Algorithms

Analysis and Comparison of Exchange Sorting Algorithms

Методика выбора алгоритмов оптимизации живучести энергетических инфраструктур

The article considers one of the most difficult tasks of studying the resilience of energy infrastructures – finding effective combinations of measures to increase resilience. To solve this problem, the article describes an approach that considers it as a problem of structural-parametric optimization of energy infrastructures, which is built according to a two- or three-level scheme. The approach described in the article adds another layer to the middle of the above scheme, which checks the efficiency of the selected equipment under extreme conditions created by a given set of large disturbances. The main disadvantage that the approach inherits from the structural-parametric optimization of energy infrastructures is a high computational complexity of the multilevel optimization scheme. However, the unacceptable calculation time can be explained by the selection of inappropriate optimization algorithms. In the papers concerning the structural-parametric optimization of energy infrastructures publ in the literature, the question of comparing optimization algorithms with each other is clearly not raised. Therefore, this article proposes a three-stage methodology for selecting optimization algorithms, according to which, before solving a specific problem of optimizing the resilience of energy infrastructures, first test the algorithms, and then choose the best one based on a multi-criteria analysis of the test results. To apply the methodology, it is necessary to develop a special lightweight version of the task of optimizing resilience and prepare a testbed for organizing and conducting test computational experiments. The application of the methodology is demonstrated by the example of choosing heuristic methods for finding optimal solutions from the PaGMO library used at the external level of the resilience optimization scheme of the Unified Gas Supply System of Russia. In total, five popular evolutionary algorithms were tested, the most suitable of which turned out to be a genetic sorting algorithm without NSGA-II dominance.

Probabilistic Modeling for Conditional Statements

A new mathematical framework is proposed in this study to comprehend the impact of program architecture on input random variables, the IF statement was the main topic. The primary idea that is theoretically and experimentally supported in this study is that the part of the joint pmf of a collection of random variables that represents the condition will be shifted to the part that represents the action. After sorting two random variables, the framework is used with four random variables, and the theoretically produced results were realistically validated. The study's equations can be applied to assessing probabilistic models of various sorting algorithms or other intricate program structures. This may also result in future investigations formalizing more precise execution time expectations.

Guidelines for the use of flow cell sorting in diagnosis and monitoring of acute leukemia

Flow cell sorting is an advanced laboratory technique that combines the analytical capabilities of flow cytometry with the ability to isolate pure cell populations from heterogeneous samples. It has tremendous potential both for fundamental research and laboratory diagnosis. For example, the combination of cell sorting and molecular genetic studies can be used to clarify ambiguous results of acute leukemia immunophenotyping obtained both at diagnosis and during minimal residual disease monitoring. These guidelines are based on years of experience in incorporating cell sorting into the diagnostic and monitoring processes at the Leukemia Immunophenotyping Laboratory of the Dmitry Rogachev National Medical Research Center of Pediatric Hematology, Oncology and Immunology. They include methods used for the confirmation of flow cytometry data depending on the type of leukemia, the stage of a flow cytometry assay and previous therapy. They also describe cell sorting algorithms for disease diagnosis and the specifics of sample preparation for cell sorting in different molecular genetic studies.

Approximate sorting and its applications in I/O model

Sorting is a fundamental component in many different applications including web indexing engines, geographic information systems, data mining and database systems. However, the existing optimal algorithms still cause huge costs when the input data becomes very large. Thus, the approximate sorting for big data is considered in this paper. The goal of approximate sorting for big data is to generate an approximate sorted result, but using less CPU and I/O cost. For big data, we consider the approximate sorting and applications for approximate sorted results in I/O model.The quality of approximate sorting results is usually measured by the distance metrics on permutation space. However, the existing metrics on permutation space are not available for external approximate sorting algorithms. Thus, we propose a new kind of metric named External metric, which ignores the errors and dislocations that happened in each I/O block. The External metric of Spearman's footrule metric is named as External Spearman's footrule metric (short as ESP metric), which is analyzed in this paper.Furthermore, to facilitate a better evaluation of the approximate sorted result, we propose a new metric, named as errors, which directly states the number of dislocation of the elements. The External errors are also considered in this paper.Then, according to the rate-distortion relationship under these two metrics, the lower bound of these two metrics on external approximate sorting problem with t I/O operations is proved. We propose a k-passes external approximate sorting algorithm, named as EASORT, and prove that EASORT is asymptotically optimal under ESP metric.Finally, we consider the applications on approximate sorting results. An index for the approximate sorted result is proposed. The single and range query on approximate sorted result using this index are also analyzed. Further, the sort-merge join on two relations, where one of the relations is approximate sorted or both relations are approximate sorted, are all discussed in this paper.

Improved A-Star Path Planning Algorithm in Obstacle Avoidance for the Fixed-Wing Aircraft

The flight management system is a basic component of avionics for modern airliners. However, the airborne flight management system needs to be improved and relies on imports; path planning is the key to the flight management system. Based on the classical A* algorithm, this paper proposes an improved A* path planning algorithm, which solves the problem of low planning efficiency and following a non-smooth path. In order to solve the problem of the large amount of data calculation and long planning time of the classical A* algorithm, a new data structure called a “value table” is designed to replace the open table and close table of the classical A* algorithm to improve the retrieval efficiency, and the Heap sort algorithm is used to optimize the efficiency of node sorting. Aiming at the problem that the flight trajectory is hard to follow, the trajectory smoothing optimization algorithm combined with turning angle limit is proposed. The gray value in the digital map is added to the A* algorithm, and the calculation methods of gray cost, cumulative cost, and estimated cost are improved, which can better meet the constraints of obstacle avoidance. Through the comparative simulation verification of the algorithm, the improved A* algorithm can significantly reduce the path planning time to 1% compared to the classical A* algorithm; it can be seen that the proposed algorithm improves the efficiency of path planning and the smoother planned path, which has obvious advantages compared to the classical A* algorithm.

Single-Instruction-Multiple-Data Instruction-Set-Based Heat Ranking Optimization for Massive Network Flow

In order to cope with the massive scale of traffic and reduce the memory overhead of traffic statistics, the traffic statistics method based on the Sketch algorithm has become a research hotspot for traffic statistics. This paper studies the problem of the top-k flow statistics based on the Sketch algorithm and proposes a method to estimate the flow heat from massive network traffic using the Sketch algorithm and identify the kth flow with the highest heat by using a bitonic sort algorithm. In view of the performance difficulties of applying multiple hash functions in the implementation of the Sketch algorithm, the Single-Instruction-Multiple-Data (SIMD) instruction set is adopted to improve the performance of the Sketch algorithm so that SIMD instructions can process multiple fragments of data in a single step, implement multiple hash operations at the same time, compare and sort multiple flow tables at the same time. Thus, the throughput of the execution task is improved. Firstly, the elements of data flow are described and stored in the form of vectors, while the construction, analysis, and operation of data vectors are realized by SIMD instructions. Secondly, the multi-hash operation is simplified into a single vector operation, which reduces the CPU computing resource consumption of the Sketch algorithm. At the same time, the SIMD instruction set is used to optimize the parallel comparison operation of the flow table in a bitonic sort algorithm. Finally, the SIMD instruction set is used to optimize the functions in the Sketch algorithm and top-k sorting algorithm program, and the optimized code is tested and analyzed. The experimental results show that the time consumed by the advanced vector extensions (AVX)-instructions-optimized version has a significant reduction compared to the original version. When the length of KEY is 96 bytes, the instructions consumed by multiple hash functions account for less in the entire Sketch algorithm, and the time consumed by the optimized version of AVX is about 67.2% of that in the original version. As the length of KEY gradually increases to 256 bytes, the time consumed by the optimized version of AVX decreases to 53.8% of the original version. The simulation results show that the AVX optimization algorithm is effective in improving the measurement efficiency of network flow.

A minority of final stacks yields superior amplitude in single-particle cryo-EM

Cryogenic electron microscopy (cryo-EM) is widely used to determine near-atomic resolution structures of biological macromolecules. Due to the low signal-to-noise ratio, cryo-EM relies on averaging many images. However, a crucial question in the field of cryo-EM remains unanswered: how close can we get to the minimum number of particles required to reach a specific resolution in practice? The absence of an answer to this question has impeded progress in understanding sample behavior and the performance of sample preparation methods. To address this issue, we develop an iterative particle sorting and/or sieving method called CryoSieve. Extensive experiments demonstrate that CryoSieve outperforms other cryo-EM particle sorting algorithms, revealing that most particles are unnecessary in final stacks. The minority of particles remaining in the final stacks yield superior high-resolution amplitude in reconstructed density maps. For some datasets, the size of the finest subset approaches the theoretical limit.

Дослідження ефективності деяких детермінованих методів передобробки сортування даних

To verify the hypothesis about decrease in time of sorting by algorithms of different computational complexity experiments have been conducted. Several ideas on deterministic preprocessing of data arrays for sorting algorithms have been tested. The following algorithms are proposed: quick preprocessing – prediction of the index of an element in a sorted array and permutation, preprocessing with memory - prediction and permutation with memorization of previously set elements, preprocessing with reordering – reverting sequences of elements sorted in reverse order. Also proposed block variations of quick and preprocessing with memory, which are performed for parts of the array of a given length. It has been defined that the higher efficiency of preprocessing is achieved by using with sorting algorithms, which are significantly accelerated on sorted (or almost sorted) arrays of data. Block preprocessing methods can be performed faster due to the possibility of avoiding cache misses, but show a lower percentage of array sorting. Experiments were conducted to evaluate the effectiveness of various sorting algorithms after and together with the proposed preprocessing methods.