Akash Kumar, Akshay Dutt, Gautam Saini et al. · 2016
Given an array with n elements, we want to rearrange them in ascending order. Sorting algorithms such as the Bubble, Insertion and Selection Sort all have a quadratic time complexity that limits their use when the number of elements is very big. In this paper, we introduce Merge Sort, a divide-and overcome algorithm to sort an N element array. We evaluate the O(NlogN)time complexity of merge sort theoretically and empirically. Our results show a large improvement in efficiency over other algorithms.
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Ramu Anandakrishnan (294535) · Figshare · 2015
<p>Consider an 8-particle system, with particle 1 being the selected particle. First, the split-merge algorithm recursively separates the particles, other than the selected particle, into a hierarchical binary tree. Next, the elementary symmetric function (ESF) for the leaf nodes, which consist of a single particle, are calculated. The ESF for all the other nodes, are then computed by recursively, starting from the bottom, merging the ESF from the two branches for each node using Eq. (21).</p>
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Peter Varman, Balakrishna R. Iyer, Don Haderle · 2002
An efficient algorithm for merging two memory-resident sorted lists is described. The algorithm is based on a novel low-cost partitioning algorithm that is used to split the two lists among an arbitrary number of processors in a way that ensures load balance during the merge. The algorithm has direct applications in memory-resident databases, as well as for handling record pointers in disk-resident databases. It may be used for parallel sorting, table access using multiple indexes, and parallel sort-merge joins. A feature of the partitioning algorithm is that it may itself be parallelized efficiently; the parallel implementation reduces partitioning time, which may become significant if the number of processors gets large. If p is the number of processors and N is the total number of elements in both runs combined, the serial and parallel versions of the partitioning algorithm require time O(p log (N/p)), and O(log p+log(N/p)), respectively.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Charu Manivannan (9726301), Jakub Krukar (9726298), Angela Schwering (14122569) · Figshare · 2024
<div><p>Sketch maps are valuable tools used across various disciplines including spatial cognition, environmental psychology, and spatial reasoning. A common approach to evaluate sketch maps in research is to align and compare them with metric maps. However, sketch maps are highly abstract and contain generalized information causing difficulty in their alignment. Current approaches to study sketch maps cannot handle generalized information. They require a one-on-one correspondence between features in the metric map and features in the sketch map. But memory is often generalized. This paper makes two contributions to the research on sketch maps: (i) we present an algorithmic approach to detect generalization in sketch maps (ii) we present an online tool that creates a generalized metric map corresponding to features in sketch maps. Previously, we identified nine types of generalization in sketch maps. In this paper, we develop formal operators to detect these generalizations and implement them as an online tool. We evaluated our algorithm with a set of 11 sketch maps containing 84 instances of generalization. The results indicated that our algorithm consistently detects instances of generalization in sketch maps.</p></div>
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Veselka Boeva, Милена Ангелова, Elena Tsiporkova · 2019
In this article we propose a bipartite correlation clustering technique that can be used to adapt the existing clustering solution to a clustering of newly collected data elements. The proposed tec ...
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Yaser Afshar (2591362), Ivo F. Sbalzarini (199208) · Figshare · 2016
<p>In the upper row, the evolving contours are shown by dashed lines and the underlying objects to be segmented by the black solid regions. (a) The situation before re-labeling the regions. Two regions (B/C) touch at a sub-image boundary, but should not fuse according to the image energy model. The region A extends across multiple sub-images and splits in sub-image 3. (b) Applying a parallel connected-component algorithm [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0152528#pone.0152528.ref030" target="_blank">30</a>] would erroneously fuse regions touching at sub-image boundaries and unnecessarily re-label all regions with new unique labels.</p>
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Anthony Mansfield · Discrete Mathematics · 1973
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Michael Cramer · Random Structures and Algorithms · 1997
The number Lk of comparisons performed by the Merge–Sort algorithm to sort 2k keys follows the recursion , where , and Yk are independent and is a copy of Lk−1. The contraction method for ideal metrics of Rachev and Rüschendorf [7] is appropriate to handle recursions of the above type and to show asymptotic normality of the normalized Lk. Additional challenges have to be faced if the number of keys is not a power of 2. The difficulty lies in the fact that the cases of odd and even numbers differ slightly. Therefore, exact calculations of mean and variance have to be substituted by asymptotic results which are gained with the help of a run of a C-program. But even in that case asymptotic normality can be achieved by a refinement of the contraction principle. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11, 81–96, 1997
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Sumit Mishra, Ved Prakash, Carlos A. Coello Coello · Lecture notes in computer science · 2025
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Oded Green, Robert Mccoll, David A. Bader · 2013
Graphics Processing Units (GPUs) have become ideal candidates for the development of fine-grain parallel algorithms as the number of processing elements per GPU increases. In addition to the increase in cores per system, new memory hierarchies and increased bandwidth have been developed that allow for significant performance improvement when computation is performed using certain types of memory access patterns. Merging two sorted arrays is a useful primitive and is a basic building block for numerous applications such as joining database queries, merging adjacency lists in graphs, and set intersection. An efficient parallel merging algorithm partitions the sorted input arrays into sets of non-overlapping sub-arrays that can be independently merged on multiple cores. For optimal performance, the partitioning should be done in parallel and should divide the input arrays such that each core receives an equal size of data to merge. In this paper, we present an algorithm that partitions the workload equally amongst the GPU Streaming Multiprocessors (SM). Following this, we show how each SM performs a parallel merge and how to divide the work so that all the GPU’s Streaming Processors (SP) are utilized. All stages in this algorithm are parallel. The new algorithm demonstrates good utilization of the GPU memory hierarchy. This approach demonstrates an average of 20X and 50X speedup over a sequential merge on the x86 platform for integer and floating point, respectively. Our implementation is 10X faster than the fast parallel merge supplied in the CUDA Thrust library.
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Kanupriya Salaria, Wiriyanto Darsono, Michael Hinman et al. · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2004
This paper describes a novel technique to detect military convoy’s moving patterns using the Ground Moving Target Indicator (GMTI) data. The specific pattern studied here is the moving vehicle groups that are merging onto a prescribed location. The algorithm can be used to detect the military convoy’s identity so that the situation can be assessed to prevent hostile enemy military advancements. The technique uses the minimum error solution (MES) to predict the point of intersection of vehicle tracks. Comparing this point of intersection to the prescribed location it can be determined whether the vehicles are merging. Two tasks are performed to effectively determine the merged vehicle group patterns: 1) investigate necessary number of vehicles needed in the MES algorithms, and 2) analyze three decision rules for clustering the vehicle groups. The simulation has shown the accuracy (88.9% approx.) to detect the vehicle groups that merge at a prescribed location.
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Jian Zhang, Rui Jin · Advances in intelligent systems and computing · 2020
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Yimei Li (778105), Matt Hall (5666026), Brian T. Fisher (830903) et al. · Figshare · 2015
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Zhen Zhang, Xiantao Lin, Kaihang Yang et al. · 2022 5th International Conference on Pattern Recognition and Artificial Intelligence (PRAI) · 2022
When a baby is sleeping in a crib, chair or bed, there may be some dangerous situations, such as choking because the baby is not strong enough to turn over and remains on his or her stomach. This study focuses on infant characteristics including behavioral characteristics (such as lying down on their stomachs, crawling, lying down, sitting, standing) and facial features (such as calm, happy, sad), based on the YOLOv5 target detection algorithm and improved it to make it more suitable for rapid and accurate detection of infant conditions. The original NMS used by original YOLOv5 is not friendly to prediction boxes with high coincidence degree. The Merge-YOLOv5 adds merge-NMS on the basis of original YOLOv5 to make the position of prediction boxes more accurate. After verification, the merge-YOLOv5 features improved by 2.5 percentage points compared with the original YOLOv5 features mAP@0.5:0.95 on average, in which the motion features of lying on the stomach get an improvement up to by 4.4 percentage points. In this way, it is proved that our MergeYOLOv5 is promising for infant monitoring.
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Mingxue Wang, Vincent Huang, Anne-Marie Cristina Bosneag · 2018
Clustering algorithms are used in a large number of big data analytic applications spread across various application domains, including network management. We propose a novel Split-merge-evolve algorithm for clustering data into k number of clusters. The algorithm randomly divides data into k clusters initially, then repeatedly splits bad clusters and merges closest clusters to evolve the final clustering result. A key metric during the clustering process of the Split-merge-evolve algorithm is a user chosen or defined clustering quality metric or internal evaluation. The algorithm evolves the clustering result towards the user expected high quality result, although there is no ground truth or labelled data involved during the clustering process. The algorithm design is flexible in its implementation, with various common techniques, such as centroid and connectivity based measures that can be used in its implementation. The algorithm is easy to implement and effective. With 4 datasets, including 2 real life datasets in our experiments, the Split-merge-evolve algorithm performs better than both most commonly used K-means and Agglomerative hierarchical algorithms.
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Khurram Shehzad Khan, Atiq Ur Rehman, Adnan Khan et al. · IEEE Transactions on Artificial Intelligence · 2024
This work proposes a novel Split and Kernel-Merge Clustering (S-KMC), a nonparametric clustering algorithm that combines the strengths of hierarchical clustering, partitional clustering, and density-based clustering. It consists of two main phases: Splitting and Merging. In the Splitting phase, a ranking-based operator is used to divide the data into optimal subclusters. In the Merging phase, a kernel function estimates the density of these subclusters after projecting them onto a straight line passing through their centers, facilitating the merging operation. S-KMC is fully nonparametric, eliminating the need for prior information about the data. It effectively handles (i) shape diversity, (ii) density variability, (iii) high dimensionality, (iv) outliers, and (v) missing values. The algorithm offers easily tunable hyperparameters, enhancing its applicability to complex problems and robustness against data anomalies. Experimental analysis on 21 benchmark datasets demonstrates the improved performance of S-KMC in terms of cluster accuracy, handling high-dimensional data, and managing data anomalies and outliers. Comprehensive comparisons with state-of-the-art techniques further validate the superior or comparable performance of the proposed S-KMC algorithm.
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Rahmadi Asri, Mahyuddin K. M. Nasution, Suherman Suherman · Journal of Physics Conference Series · 2019
Abstract The development of increasingly sophisticated technology with more intensive use of computers facilitates human work activities, so that security problems arise that misuse information that can endanger users. The third parties who commit crimes against users are called cryptanalyst. Cryptanalyst interferes with computer networks in many forms such as data theft. Cryptography is a security solution for cryptanalysts; one of them is by using the El-Gamal algorithm. Researchers have proposed El-Gamal modification with good results, but not all security problems can be solved. The algorithm cannot guarantee protection against the adaptive attack. This article proposes the application of split merge method on the El-Gamal algorithm to improve security. The study describes the system analysis and design. Since the combination uses large prime number calculations, it is expected to be effective to make cryptanalyst more difficult to break the plaintext.
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Denham Coates-evelyn · 2001
An algorithm that does O(n 2) comparisons and data moves to sort a list of n random data values on a uni-processor system is presented. We show a multiprocessor implementation that has complexity of O ( √ n) using the MIMD model on a mesh connected system. The AT 2 complexity on this model is O(n 5/2 lg(n)), which is sub-optimum by a factor of O ( √ n / lg(n)).
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Marsman, M Marcel · TU/e Research Portal (Eindhoven University of Technology) · 1996
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Sirilak Ketchaya, Apisit Rattanatranurak · Journal of Southwest Jiaotong University · 2024
Quicksort is a well-known algorithm used to solve scientific problems. It divides an input array into smaller subarrays and sorts them. However, this algorithm sorts the input data using only one thread. Thus, the algorithm can be implemented to execute in parallel to improve the sorting performance. The study developed a parallel sorting algorithm that uses a block-based concept to partition data and optimized this parallel sorting algorithm using the OpenMP scheduling type. In this study, the parallel sorting algorithm termed the parallel deque-free partition dual-deque merge sorting algorithm is proposed and executed on shared memory architecture. Deque-free partitioning (DFPar) is a parallel block-based partitioning algorithm that partitions an array in blocks without addition operations, and dual-deque merge is a merging algorithm that merges blocks of data into the correct position and sorting steps. This parallel sorting algorithm is implemented using an application programing interface that supports parallel programing on shared memory architecture named OpenMP to improve performance. In this experiment, an Intel Core i7 machine running the Ubuntu Linux operating system was used. Results show that DFPDMSort is faster than benchmarks such as the multi-way merge sort algorithm on a large data size. The performance of the Deque-Free Partitioning step is optimized by the OpenMP scheduling type and its chunk size. Moreover, the parameters of this algorithm, such as block size and cutoff size, can be used as guidelines to improve the performance of other parallel block-based algorithms. These parameters affect cache and branch load misses of the algorithm.
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