Efficient Sorting Algorithm Research Articles

An in-depth study of sorting algorithms

Sorting algorithms are very popular fundamental algorithms in the field of computer science. Its job is sorting statistics so that they are arranged according to certain rules. In this paper, the kinds of sorting algorithms and their research method of them will be discussed. It will consist of discussing bubble sort, selection sorting, insertion sorting, hill sorting, and merge sorting. Those of them are that arrange a group of elements according to a certain number of ones. They are widely used in computer science and data processing in all walks of life. The most common sorting methods are numerical order and lexicographic order. Efficient sorting algorithms are significant in some of the algorithms, such as search and merge algorithms, so that they can arrive at the correct solution. Dealing with textual data and producing readable output are also important applications of sorting. The outcome is a permutation or recombination of the original input. So learning about the principles of those sorting algorithms by recognizing the code or reading pictures is significant. It is also necessary to be familiar with the applications of those algorithms which are beneficial to the daily life.

An Efficient Algorithm for Sorting and Duplicate Elimination by Using Logarithmic Prime Numbers

Data structures such as sets, lists, and arrays are fundamental in mathematics and computer science, playing a crucial role in numerous real-life applications. These structures represent a variety of entities, including solutions, conditions, and objectives. In scenarios involving large datasets, eliminating duplicate elements is essential to reduce complexity and enhance performance. This paper introduces a novel algorithm that uses logarithmic prime numbers to efficiently sort data structures and remove duplicates. The algorithm is mathematically rigorous, ensuring correctness and providing a thorough analysis of its time complexity. To demonstrate its practicality and effectiveness, we compare our method with existing algorithms, highlighting its superior speed and accuracy. An extensive experimental analysis across one thousand random test problems shows that our approach significantly outperforms two alternative techniques from the literature. By discussing the potential applications of the proposed algorithm in various domains, including computer science, engineering, and data management, we illustrate its adaptability through two practical examples in which our algorithm solves the problem more than 3×104 and 7×104 times faster than the existing algorithms in the literature. The results of these examples demonstrate that the superiority of our algorithm becomes increasingly pronounced with larger problem sizes.

Cooperative Decision-Making Approach for Multiobjective Finite Control Set Model Predictive Control Without Weighting Parameters

Finite control set model predictive control (FCS-MPC) has gained increasing popularity as an emerging control strategy for electrical drive systems. However, it is still a challenging task to optimize weighting parameters, as multiple objectives are involved in the customized cost function. A cooperative decision-making approach for FCS-MPC is proposed in this article, to solve the optimization problems with manifold control objectives. By splitting the cost function, the optimization problem underlying multi-objective FCS-MPC is separated into a series of decomposed optimization problems. By doing so, the dimension of the decomposed problem is reduced to one. To collect the information for decision-making, an efficient sorting algorithm is applied for each control objective. The theory behind the cooperative decision-making approach is comprehensively analyzed, to validate both the effectiveness and efficiency of the proposed scheme. More specifically, the highlight is the adaptive mechanism on the number of desired candidates, to obtain a decent performance for torque and flux. The candidate which minimizes the switching frequency is selected as the optimal. The proposed scheme is experimentally verified and compared with the existing FCS-MPC without weighting parameters.

ThSORT: an efficient parallel sorting algorithm on multi-core DSPs

thSORT: an efficient parallel sorting algorithm on multi-core DSPs

Preprocessing: A method For Reducing Time Complexity

Data can be processed quickly if it is in some order, whereas unsequenced data can take more time to obtain results. Sorting is used for data arrangement. It is also one of the essential requirement for most applications and this step helps to boost performance. Sorting is also a prerequisite in several computer applications like databases. Over time computer scientists have not only introduced new sorting techniques considering various factors to be improved but they have also presented enhanced variants of existing sorting methods. The main objective has always been to reduce the execution time and space of the sorting algorithms. With every passing day, digital content is growing rapidly, which is a significant cause that encourages researchers to design new time-space efficient sorting algorithms. This paper presents some preprocessing strategies for quicksort and insertion sort to improve their performances. Tha main idea of using these preprocessings is to make input data more suitable for sorting algorithm, as most sorting function performs extraordinary for a specific type of input, such as insertion sort works better on nearyly sorted data. To authenticate the efficiency of existing sorting algorithms, these have been compared with proposed preprocessing strategies. The results with proposed techniqes outperforms the results of original sorting methods. It also helps to convert worst case into average case. By using this approch complexity of many algorithms can be reduced, therfore this is very important.

Secure word-level sorting based on fully homomorphic encryption

Fully homomorphic encryption enables to perform arbitrary computations over encrypted data opening a new avenue for the secure outsourced computation in cloud computing. Data sorting is a classical computational problem in computer science. Previously, all the secure sorting algorithms based on fully homomorphic encryption made use of the bit-level encryption, which requires that each bit of the input data is encrypted separately. However, the bit-level encryption incurs expensive computational overheads and a large ciphertext expansion. In this paper, we propose a secure word-level sorting scheme based on fully homomorphic encryption. We introduce a set of novel techniques to design an efficient word-level sorting algorithm. These include a new technique to compare two encrypted integers, a constant extraction technique to postprocess the output ciphertext of the comparison algorithm, an equality test method to check whether two ciphertexts encrypt the same integer and the single instruction multiple data technique to reduce the ciphertext sizes and improve the computational performance. The experimental results show that our word-level sorting algorithm outperforms the state-of-the-art bit-level sorting algorithm by more than 10 times.

An improved non-dominated sorting biogeography-based optimization algorithm for multi-objective land-use allocation: a case study in Kigali-Rwanda

ABSTRACT With the continuous increase of rapid urbanization and population growth, sustainable urban land-use planning is becoming a more complex and challenging task for urban planners and decision-makers. Multi-objective land-use allocation can be regarded as a complex spatial optimization problem that aims to achieve the possible trade-offs among multiple and conflicting objectives. This paper proposes an improved Non-dominated Sorting Biogeography-Based Optimization (NSBBO) algorithm for solving the multi-objective land-use allocation problem, in which maximum accessibility, maximum compactness, and maximum spatial integration were formulated as spatial objectives; and space syntax analysis was used to analyze the potential movement patterns in the new urban planning area of the city of Kigali, Rwanda. Efficient Non-dominated Sorting (ENS) algorithm and crossover operator were integrated into classical NSBBO to improve the quality of non-dominated solutions, and local search ability, and to accelerate the convergence speed of the algorithm. The results showed that the proposed NSBBO exhibited good optimal solutions with a high hypervolume index compared to the classical NSBBO. Furthermore, the proposed algorithm could generate optimal land use scenarios according to the preferred objectives, thus having the potential to support the decision-making of urban planners and stockholders in revising and updating the existing detailed master plan of land use.

AICP: Augmented Informative Cooperative Perception

Connected vehicles, whether equipped with advanced driver-assistance systems or fully autonomous, require human driver supervision and are currently constrained to visual information in their line-of-sight. A cooperative perception system among vehicles increases their situational awareness by extending their perception range. Existing solutions focus on improving perspective transformation and fast information collection. However, such solutions fail to filter out large amounts of less relevant data and thus impose significant network and computation load. Moreover, presenting all this less relevant data can overwhelm the driver and thus actually hinder them. To address such issues, we present Augmented Informative Cooperative Perception (AICP), the first fast-filtering system which optimizes the informativeness of shared data at vehicles to improve the fused presentation. To this end, an informativeness maximization problem is presented for vehicles to select a subset of data to display to their drivers. Specifically, we propose (i) a dedicated system design with custom data structure and lightweight routing protocol for convenient data encapsulation, fast interpretation and transmission, and (ii) a comprehensive problem formulation and efficient fitness-based sorting algorithm to select the most valuable data to display at the application layer. We implement a proof-of-concept prototype of AICP with a bandwidth-hungry, latency-constrained real-life augmented reality application. The prototype adds only 12.6 milliseconds of latency to a current informativeness-unaware system. Next, we test the networking performance of AICP at scale and show that AICP effectively filters out less relevant packets and decreases the channel busy time.

IN-PLACE MERGING AND EXTERNAL SORTING ALGORITHM WITH NO ADDITIONAL DISK SPACE

The performance of external sorting mainly depends on its I/O and time complexities. In this paper we represent a more efficient external sorting algorithm with no additional disk space. This algorithm uses Quick sort to produce runs in the first phase. It uses special in-place merging technique in the second phase. The algorithm excels in sorting a huge file, which is larger than the available internal memory of the computer. The algorithm creates no backup file for manipulating huge records. Usually the external sorting algorithm needs additional disk space in merging phase. This algorithm saves disk space, since it does not use any backup file or additional disk space. Here we have briefly reviewed the external sorting algorithms, which do not use additional disk space. The I/O and time complexities of the proposed algorithm are analyzed and compared with that of other similar algorithms. We have found that the I/O complexity of the proposed algorithm is less than that of other similar algorithms (algorithms which do not need additional disk space) with the same time complexity.

An Efficient Sorting Algorithm for Capacitor Voltage Balance of Modular Multilevel Converter With Space Vector Pulsewidth Modulation

Thisarticle presents an efficient analogue sorting algorithm for balancing the submodule (SM) capacitor voltages of modular multilevel converter (MMC). The proposed analogue sorting algorithm offers the advantage of fast convergence rate without any need of recursive loops for the implementation on embedded devices. It can be easily implemented with combinational logic operations on field programmable gate array (FPGA) and provides less hardware and computational overhead. The functionality and performance of the proposed analogue sorting algorithm is evaluated with the simulation model of three phase five-level MMC in MATLAB/Simulink environment. The real time implementation of the proposed sorting algorithm with the SM capacitor voltage balancing strategy is implemented on Altera/Cylone - I (EP1C12Q240C8N) FPGA. A five-level continuous space vector pulsewidth modulation (CSVPWM) is realized on a PIC microcontroller (PIC18F452). A down-scaled model of single-phase five-level MMC is designed and constructed to investigate the reliable and stable operation of MMC with the proposed analogue sorting algorithm and SVPWM method. Simulation and experimental results are presented for validation.

More Efficient Parallel Integer Sorting

We present a more efficient CREW PRAM algorithm for integer sorting. This algorithm sorts [Formula: see text] integers in [Formula: see text] in [Formula: see text] time and [Formula: see text] operations. It also sorts [Formula: see text] integers in [Formula: see text] in [Formula: see text] time and [Formula: see text] operations. Previous best algorithm [15] on both cases has time complexity [Formula: see text] but operation complexity [Formula: see text].

A General Framework for Sorting Large Data Sets Using Independent Subarrays of Approximately Equal Length

Designing an efficient data sorting algorithm that requires less time and space complexity is essential for computer science, different engineering disciplines, data mining systems, wireless networks, and the Internet of things. This paper proposes a general low-complex data sorting framework that distinguishes the sorted or similar data, makes independent subarrays approximately in equal length, and sorts the subarrays’ data using one of the popular comparison-based sorting algorithms. Two frameworks, one for serial realization and another for parallel realization, are proposed. The time complexity analyses of the proposed framework demonstrate an improvement compared to the conventional Merge and Quick sorting algorithms. Following complexity analysis, the simulation results indicate slight improvements in the elapsed time and the number of swaps of the proposed serial Merge-based and Quick-based frameworks compared to the conventional ones for low/high variance integer/non-integer data sets, in different data sizes and the number of divisions. It is about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(1-1.6\%)$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(3.5-4\%)$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(0.3-1.8\%)$ </tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(2-4\%)$ </tex-math></inline-formula> improvements in the elapsed times for 1, 2, 3, and 4 divisions, respectively for small and very large data sets in Merge-based and Quick-based scenarios. Although these improvements in serial realization are minor, making independent low-variance subarrays allows the sorted components to be extracted sequentially and gradually before the end of the sorting process. Also, it proposes a general framework for parallelizing conventional sorting algorithms using non-connected (independent) or connected (dependent) multi-core structures. As the second experiment, the numerical analyses that compare the results of the parallel realization of the proposed framework to the serial one in 1, 2, 3, and 4 divisions, show a speedup factor of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(2-4)$ </tex-math></inline-formula> for small to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(2-16)$ </tex-math></inline-formula> for very large data sets. The third experiment shows the effectiveness of the proposed parallel framework to the parallel sorting based on the random-access machine model. Finally, we prove that the mean-based pivot is as efficient as the median-based and much better than the random pivot for making subarrays of approximately equal length.

A fast and efficient tool to study the rheology of dense suspensions

A cutting-edge software that adopts an optimized searching algorithm is presented to tackle the Newton–Euler equations governing the dynamics of dense suspensions in Newtonian fluids. In particular, we propose an implementation of a fixed-radius near neighbors search based on an efficient counting sort algorithm with an improved symmetric search. The adopted search method drastically reduces the computational cost and allows an efficient parallelization even on a single node through the multi-threading paradigm. Emphasis is also given to the memory efficiency of the code since the history of the contacts among particles has to be traced to model the frictional contributions, when dealing with dense suspensions of rheological interest that consider non-smooth interacting particles. An effective procedure based on an estimate of the maximum number of the smallest particles surrounding the largest one (given the radii distribution) and a sort applied only to the surrounding particles only is implemented, allowing us to effectively tackle the rheology of non-monodispersed particles with a high size-ratio in large domains. Finally, we present validations and verification of the numerical procedure, by comparing with previous simulations and experiments, and present new software capabilities.

Why You Should Know and Not Only Use Sorting Algorithms: Some Beautiful Problems

In most programming languages, the built-in (standard library) sort() function is the most convenient and efficient way for ordering data. Many software engineers have forgotten (or never knew) the underlying algorithms. In programming contests, almost all of the tasks involving sorting can be solved with only knowing how to use the sort() function. The question might arise in young students: do we need to know how it works if we only need to use it? Also, why should we know multiple efficient sorting algorithms, is not one enough? In this paper, we help the teachers to give the best answers to these questions: some beautiful tasks where the key to the solution lies in knowing a particular sorting algorithm. In some cases, the sorting algorithms are applied as a surprisingly nice idea, for example, in an interactive task or a geometry question.

An Efficient Partial Sort Algorithm for Real Time Applications

An efficient partial sort algorithm that is less complex, and more practical to implement compared to existing partial sort algorithms especially for real time applications is presented. The proposed partial sort algorithm does not use pivots, but instead makes use of past sorting decisions to narrow the search for each new sorted element. A major advantage of the proposed partial sort algorithm is that its complexity and sorting time are fixed, and are not dependent upon the data to be sorted, unlike other algorithms. This makes it a good candidate for real time applications.

On the Performance of Mean-Based Sort for Large Data Sets

Computer and communication systems and networks deal with many cases that require rearrangement of data either in descending or ascending order. This operation is called sorting, and the purpose of an efficient sorting algorithm is to reduce the computational complexity and time taken to perform the comparison, swapping, and assignment operations. In this article, we propose an efficient mean-based sorting algorithm that sorts integer/non-integer data by making approximately the same length independent quasi-sorted subarrays. It gradually finds sorted data and checks if the elements are partially sorted or have similar values. The elapsed time, the number of divisions and swaps, and the difference between the locations of the sorted and unsorted data in different samples demonstrate the superiority of the proposed algorithm to the Merge, Quick, Heap, and conventional mean-based sorts for both integer and non-integer large data sets which are random or partially/entirely sorted. Numerical analyses indicate that the mean-based pivot is appropriate for making subarrays with approximately similar lengths. Also, the complexity study shows that the proposed mean-based sorting algorithm offers a memory complexity same as the Quick-sort and a time complexity better than the Merge, Heap, and Quick sorts in the best-case. It is similar to the Merge and Heap sorts in view of the time complexity of the worst-case much better than the Quick-sort while these algorithms experience identical complexity in the average-case. In addition to finding part by part incremental (or decremental) sorted data before reaching the end, it can be implemented by parallel processing the sections running at the same time faster than the other conventional algorithms due to having independent subarrays with similar lengths.

An Enhanced Bidirectional Insertion Sort Over Classical Insertion Sort

Sorting is a technique which is used to arrange the data in specific order. A sorting technique is applied to rearrange the elements in numerical order as ascending order or descending order or for words in alphabetical order. In this paper, we propose an efficient sorting algorithm known as Enhanced Bidirectional Insertion Sorting algorithm which is developed from insertion sort concept. A comparative analysis is done for the proposed Enhanced Bidirectional Insertion Sort algorithm with the selection sort and insertion sort algorithms. When compared to insertion sort algorithm the proposed algorithm outperforms with less number of comparisons in worst case and average case computing time. The proposed algorithm works efficiently for duplicated elements which is the advanced improvement and the results are proved.

Breaking the O(n^2) Barrier: Novel Approaches to Time Complexity Analysis in Quick Sort

The most common type of sorting algorithm used is quicksort. As the name suggests it is the one of the most fastest sorting algorithm used since the innovation of sorting. However, this sort has often been criticised for its worst-case time complexity that is O(n^2). Practically the quick sort tends to follow its average case and best-case scenarios most of the time. So practically the quick sort is the most efficient practical sorting algorithm. In this paper we will fine tune this algorithm and remove its worst-case time complexity of O(n^2) and make this the best sorting algorithm both theoretically and practically. Various techniques will be discussed from pivot fixing to randomisation and further using medians of medians.

SETNDS: A SET-Based Non-Dominated Sorting Algorithm for Multi-Objective Optimization Problems

Non-dominated sorting, used to find pareto solutions or assign solutions to different fronts, is a key but time-consuming process in multi-objective evolutionary algorithms (MOEAs). The best-case and worst-case time complexity of non-dominated sorting algorithms currently known are O(MNlogN) and O(MN2); M and N represent the number of objectives and the population size, respectively. In this paper, a more efficient SET-based non-dominated sorting algorithm, shorted to SETNDS, is proposed. The proposed algorithm can greatly reduce the number of comparisons on the promise of ensuring a shorter running time. In SETNDS, the rank of a solution to be sorted is determined by only comparing with the one with the highest rank degree in its dominant set. This algorithm is compared with six generally existing non-dominated sorting algorithms—fast non-dominated sorting, the arena’s principle sort, the deductive sort, the corner sort, the efficient non-dominated sort and the best order sort on several kinds of datasets. The compared results show that the proposed algorithm is feasible and effective and its computational efficiency outperforms other existing algorithms.

A Modified Parallel Heapsort Algorithm

Sorting is a fundamental and essential problem required in the wide range of application fields, and so many sorting algorithms have been developed. Among those algorithms, heapsort is one of the most elegant and efficient sorting algorithms. But no parallel heapsort algorithm had been presented until the authors developed a restricted parallel algorithm a few years ago. This parallel algorithm had a restriction which makes it difficult to be used universally for general data sets. So, in this article, the authors present a modified parallel algorithm which is free from such restriction and can be used for any data set. This new algorithm can achieve almost the same performance as the restricted algorithm the authors developed before.