Bucket Sort Research Articles

Enhancing Bucket Sort Efficiency: A Combinatorial Approach to Algorithm Optimization

Abstract: The efficiency of sorting algorithms is critical to numerous computational processes, including data management, search operations, and real-time applications. Among these algorithms, Bucket Sort is notable for its linear-time performance when data is uniformly distributed over a defined range. However, its efficiency suffers significantly with non-uniform data distributions, resulting in unbalanced buckets and increased sorting time. In our research, we explore how combinatorial algorithms can enhance Bucket Sort’s efficiency by optimizing bucket partitioning, dynamic allocation, and internal sorting strategies. Through rigorous mathematical proofs and analysis, we demonstrate that the application of combinatorial techniques yields substantial improvements in average-case performance, particularly in handling skewed data distributions. Practical case studies in large-scale data processing illustrate the adaptability and effectiveness of these optimizations, supporting their potential in real-world applications.

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.

Optimasi Pengurutan Data Bilangan dengan Menggabungkan Algoritma Selection Sort Hybrid dan Bucket Sort

Sorting algorithms are crucial in data processing, particularly for integer data. However, as the number of integers to be sorted increases, the sorting algorithm takes longer to complete, especially for algorithms with O(n2) complexity. This article discusses optimizing integer data sorting by combining the Selection Sort Hybrid and Bucket Sort algorithms. The study aims to test the performance of the Selection Sort Hybrid and Bucket Sort algorithms and compare them with other data sorting algorithms. The research method used is experimental quantitative research, using randomly generated data using Python. The data were tested using the Combined Selection Sort Hybrid with Bucket Sort algorithm, Selection Sort Hybrid, Quick Sort, and Merge Sort. Data analysis was done by calculating the execution time of each sorting algorithm. The results show that the Selection Sort Hybrid and Bucket Sort algorithms are faster than other sorting algorithms in testing with large and complex integer data. Therefore, combining Selection Sort Hybrid and Bucket Sort algorithms can improve the efficiency and speed of sorting complex integer data.

Sky-Sorter: A Processing-in-Memory Architecture for Large-Scale Sorting

Sorting is one of the most important algorithms in computer science. Conventional CPUs, GPUs, FPGAs, and ASICs running sorting are fundamentally bottlenecked by the off-chip memory bandwidth, because of their von-Neumann architecture. Processing-near-memory (PNM) designs integrate a CPU, a GPU or an ASIC upon an HBM for sorting, but their sorting throughput are still limited by the HBM bandwidth and capacity. In this paper, we propose a skyrmion racetrack memory (SRM) -based PIM accelerator, <i>Sky-Sorter</i> , to enhance the sorting performance of large-scale datasets. Sky-Sorter implements samplesort which involves four steps, sampling, splitting marker sorting, partitioning, and bucket sorting. An SRM-based random number generator (TRNG) is used in Sky-Sorter to randomly sample records from the dataset. Sky-Sorter divides the large dataset into many buckets based on sampled splitting markers by our proposed SRM-based partitioner. Its partitioning throughput matches the off-chip memory bandwidth. We further designed an SRM-based sorting unit (SU) to sort all records of a bucket without introducing extra CMOS logic. Our SU uses the fast in-cell insertion characteristics of SRMs to implement and perform insertsort within a bucket. Sky-Sorter employs SUs to sort all buckets simultaneously by fully utilizing large internal array bandwidth. Compared to state-of-the-art accelerators, Sky-Sorter improves the throughput per Watt by <inline-formula><tex-math notation="LaTeX">$\sim 4\times$</tex-math></inline-formula> .

Fast Line Segment Detection and Large Scene Airport Detection for PolSAR

In this paper, we propose a fast Line Segment Detection algorithm for Polarimetric synthetic aperture radar (PolSAR) data (PLSD). We introduce the Constant False Alarm Rate (CFAR) edge detector to obtain the gradient map of the PolSAR image, which tests the equality of the covariance matrix using the test statistic in the complex Wishart distribution. A new filter configuration is applied here to save time. Then, the Statistical Region Merging (SRM) framework is utilized for the generation of line-support regions. As one of our main contributions, we propose a new Statistical Region Merging algorithm based on gradient Strength and Direction (SRMSD). It determines the merging predicate with consideration of both gradient strength and gradient direction. For the merging order, we set it by bucket sort based on the gradient strength. Furthermore, the pixels are restricted to belong to a unique region, making the algorithm linear in time cost. Finally, based on Markov chains and a contrario approach, the false alarm control of line segments is implemented. Moreover, a large scene airport detection method is designed based on the proposed line segment detection algorithm and scattering characteristics. The effectiveness and applicability of the two methods are demonstrated with PolSAR data provided by UAVSAR.

Two efficient local search algorithms for the vertex bisection minimization problem

The vertex bisection minimization problem (VBMP) belongs to a family of well-known graph partitioning problems with wide applications. In this study, we developed two efficient local search algorithms for VBMP, namely, BVNSbucket and BVNSbucket2, where BVNSbucket2 is improved from BVNSbucket for large graphs. The main idea in BVNSbucket is the bucket sorting technology, which greatly reduces the calculation time of the algorithm to improve the efficiency of the algorithm. Moreover, to improve the performance on large graphs, we propose a top-swap strategy and an information perturbation strategy to improve BVNSbucket, resulting in the BVNSbucket2 algorithm. The top-swap strategy is a strategy to maintain the balance between the quality of the new solution and the time required to search for the new solution. The information perturbation strategy is used to help local search escape from local optima and restart the search in a new area. We adopted several sets of popular graph instances to evaluate our algorithms, and the experiments show that the proposed algorithms are significantly better than the current optimal algorithm for most graph instances.

English Learning Motivation of College Students Based on probability Distribution

Abstract In order to systematically study the motivation tendency of college students in English learning, researchers in various countries have used a variety of test scales to conduct a questionnaire survey on college students on the basis of understanding the current situation of practical language knowledge learning. The final results show that motivation, as a major factor affecting successful language learning, can not only arouse the interest of college students in learning, but also improve their learning efficiency in practice and development.Therefore, after understanding the bucket sorting algorithm of probability distribution, this paper, according to the types and research status of English learning motivation, uses a questionnaire to select a college student to conduct a survey on English learning motivation, so as to provide effective basis for practical education management.

Research on the Sequential Difference Histogram Failure Principle Applied to the Signal Design of Radio Frequency Stealth Radar

As electronic warfare becomes the core of modern warfare, radio frequency (RF) stealth radar is becoming the focus of modern electronic warfare. The anti-sorting strategy of RF stealth radar is a new effective method of the anti-enemy electronic reconnaissance system. Hence, research on the failure mechanism of sorting algorithms has become the cornerstone of anti-sorting technology. In this paper, the mechanism of algorithm failure is studied because the SDIF algorithm is widely used in engineering practice throughout the whole workflow of the sequential difference histogram (SDIF) algorithm, from the estimation of pulse repetition interval (PRI) destroyed by the algorithm and algorithm analysis to the staggered signal. Firstly, the working steps of the SDIF histogram sorting algorithm are considered. Key steps of signal sorting by the algorithm are analyzed, and the failure principle of the sorting algorithm is proposed. It is pointed out that if the PRI signal center value of the two groups of radars is within the tolerance range of the sorting algorithm, when the two signal center values are not of the same order of magnitude, the difference is more than 10 times, and the signal variation is less than 30% of the center value, the sorting error of the algorithm for the radar signal is at least 25%. The sorting algorithm fails to sort signals. At the same time, for the sorting failure of the staggered signal, the sub-PRI design formula of the staggered signal is proposed, and the staggered signal satisfying the design formula can make the sorting algorithm invalid. Finally, the correctness of the SDIF failure principle is further verified by formula derivation, signal design simulation and experiment. The principle of sorting failure provides theoretical support and foundation for the design of anti-sorting RF stealth signal. The principle of sorting failure makes up for the shortcomings of random signal design and improves the design efficiency of RF stealth signal.

Lightweight integrity auditing of edge data for distributed edge computing scenarios

With the increase of smart devices, edge computing is becoming a new computing paradigm that coexist with centralized cloud computing to process data distributed at the edge of the network. Based on this new paradigm, app vendors can store data replicas on geographically distributed edge servers to serve surrounding users to reduce access delay. However, since edge servers have limited storage space and computing ability, these edge data are vulnerable to various corruption. Therefore, how to efficiently audit the integrity of edge data has become an urgent problem to be solved. To tackle the Edge Data Integrity (EDI) problem, we propose a lightweight auditing scheme, namely EDI-SA. Firstly, inspired by the shuffle algorithm and the bucket sorting algorithm, we propose an improved sampling algorithm, which is a new lightweight challenge block sampling method. Secondly, based on algebraic signature, EDI-SA can achieve efficient aggregation verification and the signature computation cost is independent of the number of data blocks, which greatly reduces the computation overhead of app vendors and edge servers. Thirdly, EDI-SA supports batch auditing and provable dynamic update, app vendors can also uniquely locate the corrupted edge data. Finally, security and performance analyses demonstrate the security and effectiveness of EDI-SA.

Compensatory Model Predictive Current Control for Modular Multilevel Converter With Reduced Computational Complexity

Model predictive control (MPC) is widely used in modular multilevel converter (MMC) control because of its strong robustness, fast dynamic response, and strong stability. Traditional MPC must traverse several switch combinations to accurately regulate the output current and circulating current of the MMC. Therefore, as the number of sub-module (SM) grows, the controller’s computational complexity grows. This paper proposes a compensatory model predictive current control (CMPCC) for inner loop current control. It immediately estimates the number of SMs required by the bridge arm without scrolling optimization, reducing the amount of calculation of the system and improving the output current and circulating current tracking accuracy to the references. The objective function is established based on the system output current and internal circulation current by developing the discretization mathematical model of MMC. On the basis of minimizing the optimization scope, the compensation prediction is achieved through the volt-second balance, to achieve effective current control. Subsequently, an uneven bucket sorting algorithm is proposed to drastically eliminate the unnecessary sorting process. Finally, both a MATLAB/Simulink model and an experimental platform of MMC are built. To verify the practicality of the proposed control strategy, simulation and hardware experiments are provided.

Upper tail analysis of bucket sort and random tries

Bucket Sort is known to run in expected linear time when the input keys are distributed independently and uniformly at random in the interval [0,1). The analysis holds even when a quadratic time algorithm is used to sort the keys in each bucket. We show how to obtain linear time guarantees on the running time of Bucket Sort that hold with very high probability. Specifically, we investigate the asymptotic behavior of the exponent in the upper tail probability of the running time of Bucket Sort. We consider large additive deviations from the expectation, of the form cn for large enough (constant) c, where n is the number of keys that are sorted.Our analysis shows a profound difference between variants of Bucket Sort that use a quadratic time algorithm within each bucket and variants that use a Θ(blog⁡b) time algorithm for sorting b keys in a bucket. When a quadratic time algorithm is used to sort the keys in a bucket, the probability that Bucket Sort takes cn more time than expected is exponential in Θ(nlog⁡n). When a Θ(blog⁡b) algorithm is used to sort the keys in a bucket, the exponent becomes Θ(n). We prove this latter theorem by showing an upper bound on the tail of a random variable defined on tries, a result which we believe is of independent interest. This result also enables us to analyze the upper tail probability of a well-studied trie parameter, the external path length, and show that the probability that it deviates from its expected value by an additive factor of cn is exponentially small in Θ(n).

Grayscale-inversion and rotation invariant image description with sorted LBP features

Local binary pattern (LBP) is sensitive to inverse grayscale changes. To overcome this problem, several methods map each LBP code and its complement to the minimum one. However, without distinguishing LBP codes and their complements, these methods show limited description ability. In this paper, we introduce a generic histogram sorting method which exploits pattern transition rules to preserve the distribution information of LBP codes and their complements. Based on this method, we develop a series of sorted LBP (SLBP) descriptors, including pairwise sorted ones and fully sorted ones, which are all invariant to grayscale inversion and image rotation. Since SLBP focuses on encoding difference-sign information, it is further generalized to embed difference-magnitude LBP features to obtain complementary representations. We also propose an invariant pyramid pooling strategy to aggregate SLBP features into a pyramid image representation. Experiments on several benchmark texture databases and one newly collected image database (grayscale-inversion images, GII) demonstrate the effectiveness of our descriptors for image classification under (linear or nonlinear) grayscale-inversion and rotation changes. The source code will be available at https://github.com/stc-cqupt/slbp.

Fast adaptive phase unwrapping algorithm based on improved bucket sorting

As a key step in active structured light reconstruction technology, the phase unwrapping algorithm has a direct impact on improving measurement accuracy and efficiency. A fast adaptive phase unwrapping algorithm based on improved bucket sorting (PUIBS) is proposed, which effectively improves the relative performance of the measurement system. First, the unreliability function of a pixel is defined according to the second-order difference, and adjacent pixels are combined into a pixel group. Then adaptively construct bucket arrays with different unreliability value ranges to meet the error transfer requirements, and put the pixel groups into bucket arrays corresponding to the unreliability value ranges in turn. Finally, according to the unreliability value of the bucket array, the phase unwrapping is performed in order from small to large. A verification experiment was carried out in a single-shot structured light system. The results show that the proposed algorithm is efficient, and successfully compared with the existing phase unwrapping algorithm. At the same time, it has a good effect on phase images with phase jump and phase occlusion.

FPGA-Based modular multilevel converter (MMC) controller for efficient voltage balancing in real-time simulation

At present, the implementation of the capacitor voltage balancing controller is a great challenge for the real-time simulation of the MMC systems. In this paper, a field-programmable gate array (FPGA)-based MMC controller is presented. In order to break through the bottleneck of sort scheme in real-time simulation, an efficient sorting scheme is proposed. This scheme is integrated by bucket sort and oddeven sort. It can greatly reduce the comparison times and highly leverage the inherent parallelism in FPGA. A special storage scheme is proposed and can greatly reduce resource consumption of sub-module (SM) voltages and make the utilization of FPGA more efficient. This proposed MMC controller is implemented by high-level synthesis (HLS) and a set of optimization methods are proposed to reduce the timestep. The proposed controller offers a controller timestep of 50us on Xilinx VC709 and support for 640 SMs each bridge-arm and 6 bridge-arms in one MMC on a single board. The performance and accuracy are evaluated on a case study of a back-to-back MMC-HVDC system on ADPSS.

HBM Connect: High-Performance HLS Interconnect for FPGA HBM.

With the recent release of High Bandwidth Memory (HBM) based FPGA boards, developers can now exploit unprecedented external memory bandwidth. This allows more memory-bounded applications to benefit from FPGA acceleration. However, fully utilizing the available bandwidth may not be an easy task. If an application requires multiple processing elements to access multiple HBM channels, we observed a significant drop in the effective bandwidth. The existing high-level synthesis (HLS) programming environment had limitation in producing an efficient communication architecture. In order to solve this problem, we propose HBM Connect, a high-performance customized interconnect for FPGA HBM board. Novel HLS-based optimization techniques are introduced to increase the throughput of AXI bus masters and switching elements. We also present a high-performance customized crossbar that may replace the built-in crossbar. The effectiveness of HBM Connect is demonstrated using Xilinx's Alveo U280 HBM board. Based on bucket sort and merge sort case studies, we explore several design spaces and find the design point with the best resource-performance trade-off. The result shows that HBM Connect improves the resource-performance metrics by 6.5X-211X.

A Strategy for the Linear Time Implementation of the SMVQ Algorithm

This paper proposes a linear time implementation of the Side Match Vector Quantization (SMVQ) algorithm. It maps the side match distortion values between codewords and a boundary vector onto an order-preserving integer sequence. Hence the SMVQ algorithm’s state codebook generation step can exploit any integer sorting algorithm to improve its overall runtime complexity. The proposed SMVQ implementations utilize the bucket sort algorithm to demonstrate this concept. The experimental results show a percentage change of −84.26% for N = 1024 (46.052–7.247 s) and −94.82% for N = 4096 (998.355–51.710 s) in the average execution time of the SMVQ algorithm.

Recombinant Sort: N-Dimensional Cartesian Spaced Algorithm Designed from Synergetic Combination of Hashing, Bucket, Counting and Radix Sort

Sorting is an essential operation which is widely used and is fundamental to some very basic day to day utilities like searches, databases, social networks and much more. Optimizing this basic operation in terms of complexity as well as efficiency is cardinal. Optimization is achieved with respect to space and time complexities of the algorithm. In this paper, a novel left-field N-dimensional cartesian spaced sorting method is proposed by combining the best characteristics of bucket sort, counting sort and radix sort, in addition to employing hashing and dynamic programming for making the method more efficient. Comparison between the proposed sorting method and various existing sorting methods like bubble sort, insertion sort, selection sort, merge sort, heap sort, counting sort, bucket sort, etc., has also been performed. The time complexity of the proposed model is estimated to be linear i.e.

An effective binary artificial bee colony algorithm for maximum set k-covering problem

Given a row set M and a column set C, where each column in C covers several rows of M, the maximum set k-covering problem (MKCP) is to select k columns from C, such hat the number of rows covered by the selected columns is maximized. It can be formulated as linear integer programming, and has several real world applications. Several heuristic approaches have been previously presented for solving the MKCP. However, the obtained solution quality is not stable, and the solution time increases very quickly as the size of the instance increases. This work proposes a hybrid binary artificial bee colony algorithm (HBABC) to solve the MKCP. First, based on the characteristic of MKCP, HBABC redesigns a food source updating method. The new updating method uses the previously found solutions to guide the search. Second, to improve the exploitation ability of the HBABC, a tabu based simulated annealing (TBSA) is proposed. Moveover, we employ a bucket sorting technique to speed up the TBSA. Finally, the computational results on 75 benchmark instances demonstrate that the HBABC competes favorably with other algorithms. Specifically, our algorithm improves the best known solutions on about 20 percent of the tested instances. In addition, the HBABC performs better than two binary artificial bee colony algorithms on the tested instances.

Hybrid Bucket Sorting Method for Successive Cancellation List Decoding of Polar Codes

This letter focuses on the path metric sorting of successive cancellation list (SCL) decoder for polar codes. The metric sorter is a major challenge of SCL decoder in terms of overall latency. We propose a hybrid bucket sorting method to select $L$ unordered paths with the smallest metrics out of the $2L$ paths. Each hybrid bucket sorter (HBS) consists of an optimized bucket sorter and a half cleaner. Evaluation results indicate that the HBS outperforms state-of-the-art metric sorters in terms of latency reduction.

An interesting discussion of running time for some sorting techniques without comparison sort

Sorting is one of important techniques for computer science as well as other technology areas; sorting is used mostly in searching, database management systems, scheduling, and computing algorithms. This paper aims to analyze the timing cost for some sorting techniques without comparison sorting such as Pigeonhole sort, Counting sort, Radix sort, and Bucket sort; these are sorting techniques with linear running time. Each technique is considered in running time, in-place, stable, and extra space if possible. The main contribution of the paper is experiments of sorting techniques in 90 large size test data. This is also a useful reference for working with sorting techniques.