Array sort: an adaptive sorting algorithm on multi‐thread

Sorting algorithms play a crucial role in computing, but most are designed with rigid structure that are only efficient under certain conditions. Although some sorting algorithms perform well in some circumstances, they do not perform well on some resistant platforms. This study introduces Wall-L Merge Sort, which combines quadratic sorting with a modifiable multi-layer merging approach. By setting a single parameter, L, which determines the number of merge layers, Wall-L Sort shows a transition in the time complexity from O(n2) to without any modification in the unique idea. This degree of freedom enables a broad variety of input sizes to be encompassed and expands to several constraint platforms. The results show that Wall-L Sort and K-way Merge Sort have the built-in ability to handle different situations where other algorithms fail without assistance functions. Wall-L Merge Sort is the only sorting algorithm that combines complexity tuning, cache efficiency, recursion depth control, parallelism, and broad adaptability into one framework. It may not be the best choice for every situation, but its flexibility makes it a good fit for many different platforms, from small embedded systems to big computing systems. The theoretical and empirical evidence in this paper substantiates these advantages.

Sorting and merging are two problems that commonly arise in Computer Science especially in data processing tasks. To solve these problems, several algorithms have been developed. Similarly, existing merge and sorting algorithms have been improved to provide more efficient and accurate results. In this paper, selection and merging algorithms were developed on an octa-core processing machine using System.nanoTime methods in Java in order to compare their running times. The results obtained show that Merge Sort performs far better than selection sort with careful implementations by taking advantage of multiple processing cores in the test machine and some concurrency utility in Java. It was concluded that implementing algorithms using a machine with multiple numbers of cores in their Central Processing Unit (CPU) will result in a significant improvement in the performance of both algorithms.

Enhanced Merge Sort- A New Approach to the Merging Process

We have a lot of sorting algorithms in practice in this modern informatica world. Most of them are operating in quadratic time, some have managed to get them down to logarithmic time combined with linear, but there is no sorting algorithm that is efficient enough to sort data in linear time alone. In this paper, we will try to devise some mathematical support to the failure of minimalizing the sorting algorithms in linear time by comparing three well-known approximations of ! with detailed mathematical proofs associated with it. Further, this paper deals with detailed mathematical analysis to support the fact the minimum time complexity that can be attained by a sorting algorithm is of order O( ) without taking into account any extrapolated system advancement or computer architecture modification. There are various sorting algorithms like Merge sort, Heap sort, Interpolation sort, etc. which attains this minimum possible time complexity (worst case). But if we consider some biased cases then better time complexity can be obtained. If the elements of the array are in arithmetic progression, then interpolation search takes lesser time and there are many such biased cases where a particular algorithm gives better output but this paper deals with the general case i.e., no conditions are imposed on the elements of the array.

Research on sorting algorithms is a very core research field in computer science. Today, any advancement in sorting algorithms would lead to less time and space required to perform the sorting task. This paper discusses a newly proposed algorithm—‘ledger-based sorting algorithm’. It is basically an advancement to ‘counting sort’, but not exactly counting sort. The purpose of this paper is to reduce the time and space required for sorting when the numbers given to you belong to a particular range (0–n) and all of them are distinct. This paper also compares the newly proposed algorithm with insertion sort, bubble sort, selection sort, quick sort, merge sort and mainly counting sort through graphical time analysis of these algorithms. The paper especially compares counting sort algorithm with the proposed algorithm in terms of both time and space complexity.

An alternative taxonomy (to that of Knuth and others) of sorting algorithms is proposed. It emerges naturally out of a top-down approach to the derivation of sorting algorithms. Work done in automatic program synthesis has produced interesting results about sorting algorithms that suggest this approach. In particular, all sorts are divided into two categories: hardsplit/easyjoin and easysplit/hardjoin. Quicksort and merge sort, respectively, are the canonical examples in these categories. Insertion sort and selection sort are seen to be instances of merge sort and quicksort, respectively, and sinking sort and bubble sort are in-place versions of insertion sort and selection sort. Such an organization introduces new insights into the connections and symmetries among sorting algorithms, and is based on a higher level, more abstract, and conceptually simple basis. It is proposed as an alternative way of understanding, describing, and teaching sorting algorithms.

Recent work by Google DeepMind introduced assembly-optimized sorting networks that achieve faster performance for small fixed-size arrays (3-8). In this research, we investigate the integration of these networks as base cases in classical divide-and-conquer sorting algorithms, specifically Merge Sort and Quick Sort, to leverage these efficient sorting networks for small subarrays generated during the recursive process. We conducted benchmarks with 11 different optimization configurations and compared them to classical Merge Sort and Quick Sort. We tested the configurations with random, sorted and nearly sorted arrays.

Merging and sorting algorithms are the backbone of many modern computer applications. As such, efficient implementations are desired. Recent architectural advancements in CPUs (Central Processing Units), such as wider and more powerful vector instructions, allow for algorithmic improvements. This paper presents a new approach to merge sort using vector instructions. Traditional approaches to vectorized sorting typically utilize a bitonic sorting network (Batcher's Algorithm) which adds significant overhead. Our approach eliminates the overhead from this approach. We start with a branch-avoiding merge algorithm and then use the Merge Path algorithm to split up merging between the different SIMD lanes. Testing demonstrates that the algorithm not only surpasses the SIMD based bitonic counterpart, but that it is over 2.94X faster than a traditional merge, merging over 300M keys per second in one thread and over 16B keys per second in parallel. Our new sort reaches is over 5X faster than quicksort and 2X faster than Intel's IPP library sort, sorting over 5.3M keys per second for a single processor and in parallel over 500M keys per second and a speedup of over 2x from a traditional merge sort.

We present LCP Merge, a novel merging algorithm for merging two ordered sequences of strings. LCP Merge substitutes string comparisons with integer comparisons whenever possible to reduce the number of character-wise comparisons as well as the number of key accesses by utilizing the longest common prefixes (LCP) between the strings. As one of the applications of LCP Merge, we built a string merge sort based on recursive merge sort by replacing the merging algorithm with LCP Merge and we call it LCP Merge sort. In case of sorting strings, the computational complexity of recursive merge sort tends to be greater than O(n lg n) because string comparisons are generally not constant time and depend on the properties of the strings. However, LCP Merge sort improves recursive merge sort to the extent that its computational complexity remains O(n lg n) on average. We performed a number of experiments to compare LCP Merge sort with other string sorting algorithms to evaluate its practical performance and the experimental results showed that LCP Merge sort is efficient even in the real-world.

Sorting is one of the most frequent concerns in Computer Science, various sorting algorithms were invented for specific requirements. As these requirements and capabilities grow, sequential processing becomes inefficient. Therefore, algorithms are being enhanced to run in parallel to achieve better performance. Performing algorithms in parallel differ depending on the degree of multi-threading. This study determines the optimal number of threads to use in parallel merge sort. Furthermore, it provides a comparative analysis of various degrees of multithreading. The implementation in this empirical experiment takes a group of devices with various specifications. For each device, it takes fixed-sized data set and executes merge sort for sequential and parallel algorithms. For each device, the lowest average runtime is used to measure the efficiency of the experiment. In all experiments, single-threaded is more efficient when the data size is less than 105 since it claimed 53% of the lowest runtime than the multithreaded executions. The overall average of the experiments shows either four or eight threads, with 72% and 28%, respectively, are most efficient when data sizes exceed 105.

This paper presents the study of implementation and performance in sorting process, using two different algorithms, namely Insertion Sort and Merge Sort. In the first stage, the two algorithms were implemented in C++ language to sort several numbers typed by a user. In the second stage, the source codes for those algorithms were modified to enable sorting randomly generated numbers with the amount as requested by the user. To find out how well they performed in sorting out the data, therefore in the last stage the two algorithms were tested to sort random numbers with predetermined amount ranges and the results were compared. From the experiments performed, merge sort algorithm had shown a better performance, particularly in a large number of data (> 10000). Insertion sort algorithm has the advantage in lower complexity algorithm, notably in the best case condition and since it does not use recursion routines in sorting process, hence it does not require as much storage space or memory as needed by merge sort algorithm.

Quick sort is one of the most sought after algorithms, because if implemented properly quick sort could be much faster than its counterparts, merge sort and heapsort. The main crux of quick sort algorithm is the implementation of the partitioning operation. Nico Lomuto and C. A. R Hoare have put forth partitioning algorithms that have gained prominent significance. Despite this, one can always shed more light on this partially understood operation of partition. Sorting algorithms have been further developed to enhance its performance in terms of computational complexity, memory and other factors. The proposed method is the use of randomized pivot in the implementation of Lomuto partition and Hoare partition algorithms, respectively. It is analysed with and without a randomized pivot element. This paper presents a comparison of the performance of a quick sort algorithm in different cases using contrasting partition approaches with and without randomized pivot. The results provide a theoretical explanation for the observed behaviour and give new insights on behaviour of quick sort algorithm for different cases. The Hoare partition approach with randomized pivot gives best time complexity in comparison to the other cases.

Quicksort is an important algorithm that uses the divide and conquer concept, and it can be run to solve any problem. The performance of the algorithm can be improved by implementing this algorithm in parallel. In this paper, the parallel sorting algorithm named the Multi-Deque Partition Dual-Deque Merge Sorting algorithm (MPDMSort) is proposed and run on a shared memory system. This algorithm contains the Multi-Deque Partitioning phase, which is a block-based parallel partitioning algorithm, and the Dual-Deque Merging phase, which is a merging algorithm without compare-and-swap operations and sorts the small data with the sorting function of the standard template library. The OpenMP library, which is an application programming interface used to develop the parallel implementation of this algorithm, is implemented in MPDMSort. Two computers (one with an Intel Xeon Gold 6142 CPU and the other with an Intel Core i7-11700 CPU) running Ubuntu Linux are used in this experiment. The results show that MPDMSort is faster than parallel balanced quicksort and multiway merge sort on the large random distribution data. A speedup of 13.81times and speedup per thread of 0.86 can be obtained. Thus, developers can use these parallel partitioning and merging algorithms to improve the performance of related algorithms.

Texas Instruments development kits have a wide application in practical and scientific experiments due to their small size, processing power, available booster packs, and compatibility with different environments. The most popular integrated development environments for programming these development kits are Energia and Code Composer Studio. Unfortunately, there are no existing studies that compare the benefits and drawbacks of these environments and their performances. Conversely, the performances of the FreeRTOS environment are well-explored, making it a suitable baseline for embedded systems execution. In this paper, we performed the experimental evaluation of the performance of Texas Instruments MSP-EXP432P401R when using Energia, Code Composer Studio, and FreeRTOS for program execution. Three different sorting algorithms (bubble sort, radix sort, merge sort) and three different search algorithms (binary search, random search, linear search) were used for this purpose. The results show that Energia sorting algorithms outperform other environments with a maximum of 400 elements. On the other hand, FreeRTOS search algorithms far outperform other environments with a maximum of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{2 5 5, 0 0 0}$</tex> elements (whereas this maximum was <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{1 0, 0 0 0}$</tex> elements for other environments). Code Composer Studio resulted in the largest processing time, which indicates that the lowlevel registry editing performed in this environment leads to significant performance issues.

В данной статье проводится анализ производительности различных алгоритмов сортировки в языке программирования JavaScript. Рассмотрены популярные алгоритмы, такие как сортировка вставками, выбором, слиянием, быстрая сортировка и сортировка счетчиком. Каждый алгоритм проанализирован с точки зрения времени выполнения и эффективности для различных размеров и типов данных.