Heapsort Research Articles

Comparative Analysis of Sorting Algorithms: TimSort Python and Classical Sorting Methods

The sorted() function within the Python programming language has emerged as the primary choice among developers for sorting operations. Consequently, this study offers a comparative analysis of various classical sorting algorithms and Python's built-in sorting mechanisms, with the objective of identifying the most time-efficient sorting algorithm. The analysis involves assessing the time complexity of each algorithm while handling data arrays ranging from 10 to 1,000,000 elements using Python. These arrays are populated with randomly generated numeric values falling within the range of 1 to 1000. The benchmark algorithms utilized encompass Heap Sort, Shell Sort, Quick Sort, and Merge Sort. A looping mechanism is applied to each algorithm, and their execution speeds are gauged utilizing the Python 'time.perf_counter()' library. The findings of this study collectively indicate that Python's standard algorithm, surpasses classic sorting algorithms, including Heapsort, Shellsort, Quicksort, and Mergesort, in terms of execution.

Research Paper on Visualization of Sorting Algorithm

In the realm of sorting algorithms, visualization projects serve as educational tools to comprehend and demonstrate various sorting techniques. This paper presents an analysis and review of sorting visualization projects that do not utilize parallelism. By exploring sorting algorithms without parallel processing, this review aims to provide insights into the efficiency, functionality, and visual representation of these algorithms. Understanding sorting algorithms without parallelism contributes to a foundational understanding of their sequential execution and computational complexities. Keywords: Sorting Algorithms, React Visualizer, Selection Sort, Merge Sort, Bubble Sort, Insertion Sort, Heap Sort.

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.

Algorithm Visualizer

Abstract: In recent years, computer science education has become increasingly important as technology continues to play a dominant role in our lives. The understanding of algorithms and their implementation is a crucial aspect of computer science education. Visualizing algorithms can be a powerful tool to help students understand and retain the concepts behind them. This paper presents a new algorithm visualizer that focuses on two main types of algorithms: sorting algorithms and graph pathfinding algorithms. The algorithm visualizer was created using React.js, a popular JavaScript library, and provides visualizations for various sorting algorithms, such as merge sort, quick sort, heap sort, and bubble sort. Additionally, the visualizer includes visualizations for graph pathfinding algorithms such as breadth-first search, depth-first search, and A*. The visualizer also includes mazes and patterns that can be solved using the pathfinding algorithms, allowing users to see the algorithms in action. The algorithm visualizer provides a user-friendly interface that allows users to step through the algorithms and see how they work. This interactive approach to learning algorithms provides a valuable resource for students and educators alike. The visualizer is also highly customizable, allowing users to adjust the speed and complexity of the algorithms to fit their needs. This paper provides a comprehensive overview of the design, implementation, and evaluation of the algorithm visualizer.

Research on optimal path planning technology for vehicle positioning and navigation system

Abstract Intelligent Transportation System (ITS) is created in the context of the full development and progress of contemporary science and technology, aiming to help people make the best choice, drive the best vehicle, and control the best road network traffic. Intelligent vehicle positioning and navigation system is a high-tech integrated system that applies automatic vehicle positioning technology, geographic information system and database technology, computer technology, multimedia technology, and modern communication technology. In this paper, based on the research of GPS and GIS technology, by analyzing and comparing the advantages and disadvantages of different optimal path planning algorithms, we propose to optimize the A* algorithm by using the minimum heap sorting method for nodes and combining the twoway search and hierarchical search strategies to complete the improvement of the A* algorithm. The experimental results show that the path search speed of the improved algorithm has been significantly improved and the path design optimization is obvious. The improvement algorithm proposed in this paper is feasible and reasonable, which is good for upgrading the in-vehicle navigation system and relieving urban traffic congestion.

Bayesian inversion of log-normal eikonal equations

We study the Bayesian inverse problem for inferring the log-normal slowness function of the eikonal equation, given noisy observation data on its solution at a set of spatial points. We contribute rigorous proofs on the existence and well-posedness of the problem. We then study approximation of the posterior probability measure by solving the truncated eikonal equation, which contains only a finite number of terms in the Karhunen–Loeve expansion of the slowness function, by the fast marching method (FMM). The error of this approximation in the Hellinger metric is deduced in terms of the truncation level of the slowness and the grid size in the FMM resolution. It is well known that the plain Markov chain Monte Carlo (MCMC) procedure for sampling the posterior probability is highly expensive. We develop and justify the convergence of a multilevel MCMC method. Using the heap sort procedure in solving the forward eikonal equation by the FMM, our multilevel MCMC method achieves a prescribed level of accuracy for approximating the posterior expectation of quantities of interest, requiring only an essentially optimal level of complexity. Numerical examples confirm the theoretical results.

Theoretical Analysis of Standard Selection Sort Algorithm

Sorting algorithms plays an important role in the computer science field. Many applications use sorting algorithm. There are several sorting algorithms proposed by experts, namely bubble sort, exchange short, insertion short, heap sort, quick short, merge sort, standard selection sort. One well-known algorithm of sorting is selection sort. In this journal, discussion about standard selection sort is given with thorough analysis. Sorting is very important data structure concepts that has an important role in memory management, file management, in computer science in general, and in many real-life applications. Different sorting algorithms have differences in terms of time complexity, memory use, efficiency, and other factors. There are many sorting algorithms exist right now in the computer science field. Each algorithm has its benefits and limitations where a trade-off exists between execution time and the nature of the complexity of the algorithm itself. The method is theoretical analysis. Three theoretical analyses are given with deep explanation and analysis. Each with six index arrays, namely with six data on it. The numbers are sorted in ascending order. Pseudo code is also given, to understand this algorithm more thoroughly. It is concluded that this theoretical analysis explained the algorithm more clearly, by using process iteration by hand.

Research on the Path Planning of Unmanned Sweepers Based on a Fusion Algorithm

Path planning is one of the key technologies for unmanned driving. However, global paths are unable to avoid unknown obstacles, while local paths tend to fall into local optimality. To solve the problem of unsmooth and inefficient paths on multi-angle roads in a park which cannot avoid unknown obstacles, we designed a new fusion algorithm based on the improved A* and Open_Planner algorithms (A-OP). In order to make the global route smoother and more efficient, we first extracted the key points of the A* algorithm and improved the node search structure using heap sorting, and then improved the smoothness of the path using the minimum snap method; secondly, we extracted the key points of the A* algorithm as intermediate nodes in the planning of the Open_Planner algorithm, and used the A-OP algorithm to implement the path planning of the unmanned sweeper. The simulation results show that the improved A* algorithm significantly improved the planning efficiency, the nodes are less computed and the path is smoother. The fused A-OP algorithm not only accomplished global planning effectively, but also avoided unknown obstacles in the path.

Central difference information filtering phase unwrapping algorithm based on deep learning

This paper presents a deep learning-based central difference information filtering phase unwrapping algorithm. First, the central difference information filter (CDIF) is introduced into phase unwrapping for wrapped phase images for the first time to our knowledge, and is combined with an efficient local phase gradient estimation technique, and an efficient path-following strategy based on heap sorting to construct a CDIF phase unwrapping procedure. Second, a region segmentation model based on deep learning is constructed to divide the wrapped phase images into a series of segmented regions along the edge of interferometric fringes, which is beneficial to improve the accuracy and efficiency of subsequent phase unwrapping. Finally, each segmented region of the wrapped phase images is unwrapped separately using the CDIF phase unwrapping procedure, and the unwrapping results of each segmented region are combined according to the phase consistency criterion of adjacent regions of the wrapped phase images to obtain the unwrapped phase of the whole wrapped phase images. Results delivered by the experiments on synthetic data and experimental data demonstrate the robustness and acceptable efficiency of the proposed method in phase unwrapping for the wrapped phase images, compared with some commonly used algorithms.

A-star Optimization with Heap-sort Algorithm on NPC Character

Objectives: To find out whether the A-star algorithm that is optimized with the heap-sort algorithm can reach the target destination faster than the native Astar when applied on NPC to find the path. Methods: Comparisons are made by implementing an optimized A-star algorithm with heap-sort and native Astar on an NPC in a dungeon-crawling game genre by applying five different scenarios, where each scenario has a different start position of the NPC, and the target goal is set. The comparison is made by measuring the time required by both algorithms to reach the target goal in milliseconds with Unity engine software and C# language. Findings: From the results of experiments and calculation, it was found that the A-star algorithm optimized with the heap-sort algorithm was 50%-80% faster than using only the A-star algorithm in cases that was applied alone on NPC in dungeon-crawling game. Novelty: The novelty in this research is the optimization of the A-star algorithm with heap-sort, and then that algorithm is compared with the native A-star algorithm that is applied to NPCs in the dungeon-crawling game genre. Keywords: AStar; Heap Sort; NonPlayable Character; Optimization Algorithm; Pathfinding

Lossless Compression of Hyperspectral Imagery by Assimilating Decorrelation and Pre-processing with Efficient Displaying Using Multiscale HDR Approach

The instinctive essence of the Hyperspectral imagery cube is its immense information having both spatial and spectral correlation. In the interest of reducing the storage and bandwidth requisites, an effective lossless Hyperspectral compression system is proposed. The imagery is enforced to preprocessing stage preceding decorrelation. Preprocessing stage comprises band normalization and band ordering techniques. A technique named Greedy heap sorting is addressed to sort the bands. The proposed plan accords with a Compression ratio (CR) of 8.12 and bits per pixel (bpp) of 1.67. The performance of the system is comparable to earlier algorithms for lossless Hyperspectral image compression concerning compression ratio and bpp. An experiment conducted on AVIRIS images substantiates that the methodology presented surpasses the IP3-OBPS-BPS method by a percentage increase of 116.44 in CR and a percentage decrease of 58.49 in bpp. The multiscale High Dynamic Range (HDR) approach is used to project Hyperspectral images on devices with Low Dynamic Range (LDR) devices. The Bilateral filter is used for the decomposition of the image into multiple base layers and detail layer. The PSNR obtained is 37.4911 for the compressed HDR image, which signifies the better quality of the reconstructed image with a 4.8% compression ratio.

Seismic source location using the shortest path method based on boundary discretisation scheme for microseismic monitoring in underground mines

In seismic monitoring at underground mines, the velocity models can be highly complex, particularly in presence of major geological structures . In practice, homogeneous velocity models have been widely used for the purposes of seismic event location in mine seismology . Although heterogeneous velocity models can be incorporated, ray tracing methods need be adopted in these velocity models to compute the travel times for accurately locating seismic events. These methods require each geological unit to be discretised to grids (corner-node or center-node discretisation scheme), which requires large computational capacity. In this research, the Shortest Path Method (SPM) (Moser, 1991) based on a novel Boundary Discretisation Scheme (BDS) is proposed to compute the travel times for seismic event location in heterogeneous velocity models. Only the boundaries of each geological unit are discretised to nodes. The graphical network is constructed by establishing ray paths between discretised nodes on the boundaries of geological units. Dijkstra’s algorithm (Dijkstra et al., 1959) using heap sorting method (Cao et al., 1993) is applied to search for the shortest ray paths with the first arrivals for seismic event location. The accuracy and efficiency of this method are validated using a 2D synthetic example. The seismic events recorded during the field monitoring of a dyke-roadway intersected area are located with the proposed BDS-SPM method. The results demonstrate that, compared with the conventional location method using homogeneous velocity models, the proposed method can provide more accurate seismic event locations for microseismic monitoring in underground mines.

Implementation Of Bubble Sort Algorithm On 2 Fruit Models Of Data Selection Using The Java Program Language

There are various kinds of data sorting methods that we know of which are the Bubble Sort, Selection Sort, Insertion Sort, Quick Sort, Shell Sort, Heap Sort, and Radix Sort methods. All of these methods have advantages and disadvantages of each, whose use is determined based on needs. Each method has a different algorithm, where different algorithms affect the execution time. One interesting algorithm to be implemented on 2 variant models of data sorting is the Bubble Sort algorithm, the reason is that this algorithm has a fairly long and detailed process flow to produce an ordered data sequence from a previously unordered data sequence. Two (2) data sorting variant models that will be implemented using the Bubble Sort algorithm are: Ascending data sorting variants moving from left to right, and Descending data sorting variants moving from left to right. And the device used in implementing the Bubble Sort algorithm is the Java programming language.

Application of Fibonacci heap to fast marching method

Abstract The fast marching method (FMM) is an efficient, stable and adaptable travel time calculation method. In the realization of this method, it is necessary to select the minimum travel time node from the narrow band many times. The selection method has an important influence on the calculation efficiency of FMM. Traditional FMM adopts the binary tree heap sorting method to achieve this step. Fibonacci heap sort method to FMM will be applied in this study. Compared with the binary tree heap sorting method, the Fibonacci heap sort method can realize the minimum travel time node selection in the narrow band in a more efficient way when the number of the narrow-band nodes is huge. The new method will be verified through error analysis and two numerical model calculations.

Performance Analysis of Heap Sort and Insertion Sort Algorithm

In the era of new technology, we have huge amount of data to deal with arranging the huge amount of data has remained a big challenge. This research paper includes two types of sorting algorithm, Heap Sort and Insertion Sort and also their performance analysis on thebasis of running time along with their complexity. This paper includes the algorithms and theirimplementation in Java programming language. For theresults of this research study,the comparison ofthese two sorting algorithms with different type of the data at running time such as Large, Average, and Small. In Large,data pass100 integers in the array. For Average data pass 50integers in the array and for Small data pass10 integers in the array. It checks that,which sorting technique is efficient according to the input data. Then identifiesthe efficiency of these algorithms according to this data three cases used that is Best, Average and Worst Case. The result of this analysis is showing with the help of graphs to show that how much time both algorithms take while given the desired output

Comparison of Bubble and Insertion Sort in Rust and Python Language

Sorting is the basic activity in the field of computer science and it is commonly used in searching for information and data. The main goal of sorting is to make reports or records easier to edit, delete and search, etc. It organizes the given data in any sequence. There are many sorting algorithms like insertion sort, bubble sort, radix sort, heap sort, and so forth. Bubble sort and insertion sort are clearly described with algorithms and examples. In this paper, the bubble sort and insertion sort performance analysis is carried out by calculating the time complexity. These algorithm time complexities have been calculated by implementing in the rust and python languages and observed the best case, average case, and worst case. The flowchart shows the complete workflow of this study. The results have been shown graphically and time complexity has been shown in a tabular form. We have compared the efficiency of bubble sort and insertion sort algorithms in the rust and python platforms. The rust language is more efficient than python for both bubble and insertion sort algorithms. However, it is observed insertion sort is more efficient than the bubble sort algorithm.

Efficient seismic ray tracing based on the shortest path method

SUMMARYLimiting the number of valid nodes around a reference ray can greatly reduce the calculation time of the shortest-path method (SPM). The calculation is executed by increasing the number of cells and/or nodes in the target area, step by step, until the rays converge. The ray obtained in the previous step is used as a reference ray, and the initial reference rays are given by the ordinary SPM. The Dijkstra algorithm and binary heap sorting method are used, as in the ordinary SPM. As the cell and node numbers increase, the calculation time for the modified SPM (mSPM) is reduced compared to that for the ordinary SPM. In the 3-D (100 × 100 × 100 km3) checkerboard velocity pattern model, the relative calculation time becomes two to four orders of magnitude smaller. The calculation time for the mSPM itself is approximately proportional to E log2(V), where E is the edge (ray path segment) number and V is the vertex (node) number, as seen in the heap sorting algorithm. The mean traveltime and ray path differences between the mSPM and pseudo-bending method (PBM) are small, less than 0.005 s and around 0.6 km, respectively, and slightly larger than those with respect to the ordinary SPM. The total differences from the exact solution are estimated to be less than 0.01 s and 1.0 km, which are sufficiently small for traveltime tomography. The traveltime and ray path can be improved by utilizing iterative calculations, shifting of the starting point and more neighbour nodes. The ray path obtained by the mSPM can be a local minimum, according to velocity models. The relative mean traveltime and ray path differences between adjacent cells and nodes generally show trends similar to those of the traveltime and ray path differences from the PBM. Hence, these relative differences can help reveal the behaviour of the differences from the PBM.

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.

PERFORMANCE APPRAISAL OF TREAP AND HEAP SORT ALGORITHMS

The task of storing items to allow for fast access to an item given its key is an ubiquitous problem in many organizations. Treap as a method uses key and priority for searching in databases. When the keys are drawn from a large totally ordered set, the choice of storing the items is usually some sort of search tree. The simplest form of such tree is a binary search tree. In this tree, a set X of n items is stored at the nodes of a rooted binary tree in which some item y ϵ X is chosen to be stored at the root of the tree. Heap as data structure is an array object that can be viewed as a nearly complete binary tree in which each node of the tree corresponds to an element of the array that stores the value in the node. Both algorithms were subjected to sorting under the same experimental environment and conditions. This was implemented by means of threads which call each of the two methods simultaneously. The server keeps records of individual search time which was the basis of the comparison. It was discovered that treap was faster than heap sort in sorting and searching for elements using systems with homogenous properties.
 

A Flexible and Efficient Real-Time ORB-Based Full-HD Image Feature Extraction Accelerator

This article proposes a hardware accelerator for image feature extraction based on the oriented features from accelerated segment test (FAST) and rotated binary robust independent elementary features (ORB) algorithm. The architecture adopts a hybrid workflow to process three scales in parallel as an octave, and multiple octaves are processed in serial by time-sharing the DRAM. In order to support any image resolution, a block-wise dataflow is used on the serial-parallel architecture. The overlapped data between two blocks is reused. As a result, the on-chip memory is limited to 1.47 Mb, and the DRAM bandwidth is compressed by 33%. Besides, 3×3 nonmaximum suppression with heap sorting is applied to balance keypoint distribution in 2-D. It improves the valid keypoint match ratio by 7.09%. In addition, parallel processing in keypoint detection increases 2× throughout. Moreover, approximate computing and superscalar processing reduce the timing cost in orientation estimation and descriptor generation by 92.78% and 67% respectively. Compared to the non-optimized baseline architecture, the proposed architecture saves the total timing cost by 82.4%. The accelerator is implemented in a Xilinx MPSoC, and it achieves 108 fps on full-HD images at 200 MHz under 873 mW.