Bitonic Sorting Algorithm: a Review
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An Evolutionary Approach for Sorting Algorithms
ORIENTAL JOURNAL OF ISSN: 0974-6471 COMPUTER SCIENCE & TECHNOLOGY December 2014, An International Open Free Access, Peer Reviewed Research Journal Vol. 7, No. (3): Published By: Oriental Scientific Publishing Co., India. Pgs. 369-376 www.computerscijournal.org Root to Fruit (2): An Evolutionary Approach for Sorting Algorithms PRAMOD KADAM AND Sachin KADAM BVDU, IMED, Pune, India. (Received: November 10, 2014; Accepted: December 20, 2014) ABstract This paper continues the earlier thought of evolutionary study of sorting problem and sorting algorithms (Root to Fruit (1): An Evolutionary Study of Sorting Problem) [1]and concluded with the chronological list of early pioneers of sorting problem or algorithms. Latter in the study graphical method has been used to present an evolution of sorting problem and sorting algorithm on the time line. Key words: Evolutionary study of sorting, History of sorting Early Sorting algorithms, list of inventors for sorting. IntroDUCTION name and their contribution may skipped from the study. Therefore readers have all the rights to In spite of plentiful literature and research extent this study with the valid proofs. Ultimately in sorting algorithmic domain there is mess our objective behind this research is very much found in documentation as far as credential clear, that to provide strength to the evolutionary concern2. Perhaps this problem found due to lack study of sorting algorithms and shift towards a good of coordination and unavailability of common knowledge base to preserve work of our forebear platform or knowledge base in the same domain. for upcoming generation. Otherwise coming Evolutionary study of sorting algorithm or sorting generation could receive hardly information about problem is foundation of futuristic knowledge sorting problems and syllabi may restrict with some base for sorting problem domain1. -
Improving the Performance of Bubble Sort Using a Modified Diminishing Increment Sorting
Scientific Research and Essay Vol. 4 (8), pp. 740-744, August, 2009 Available online at http://www.academicjournals.org/SRE ISSN 1992-2248 © 2009 Academic Journals Full Length Research Paper Improving the performance of bubble sort using a modified diminishing increment sorting Oyelami Olufemi Moses Department of Computer and Information Sciences, Covenant University, P. M. B. 1023, Ota, Ogun State, Nigeria. E- mail: [email protected] or [email protected]. Tel.: +234-8055344658. Accepted 17 February, 2009 Sorting involves rearranging information into either ascending or descending order. There are many sorting algorithms, among which is Bubble Sort. Bubble Sort is not known to be a very good sorting algorithm because it is beset with redundant comparisons. However, efforts have been made to improve the performance of the algorithm. With Bidirectional Bubble Sort, the average number of comparisons is slightly reduced and Batcher’s Sort similar to Shellsort also performs significantly better than Bidirectional Bubble Sort by carrying out comparisons in a novel way so that no propagation of exchanges is necessary. Bitonic Sort was also presented by Batcher and the strong point of this sorting procedure is that it is very suitable for a hard-wired implementation using a sorting network. This paper presents a meta algorithm called Oyelami’s Sort that combines the technique of Bidirectional Bubble Sort with a modified diminishing increment sorting. The results from the implementation of the algorithm compared with Batcher’s Odd-Even Sort and Batcher’s Bitonic Sort showed that the algorithm performed better than the two in the worst case scenario. The implication is that the algorithm is faster. -
A Proposed Solution for Sorting Algorithms Problems by Comparison Network Model of Computation
International Journal of Scientific & Engineering Research Volume 3, Issue 4, April-2012 1 ISSN 2229-5518 A Proposed Solution for Sorting Algorithms Problems by Comparison Network Model of Computation. Mr. Rajeev Singh, Mr. Ashish Kumar Tripathi, Mr. Saurabh Upadhyay, Mr.Sachin Kumar Dhar Dwivedi Abstract:-In this paper we have proposed a new solution for sorting algorithms. In the beginning of the sorting algorithm for serial computers (Random access machines, or RAM’S) that allow only one operation to be executed at a time. We have investigated sorting algorithm based on a comparison network model of computation, in which many comparison operation can be performed simultaneously. Index Terms Sorting algorithms, comparison network, sorting network, the zero one principle, bitonic sorting network 1 Introduction 1.2 The output is a permutation, or reordering, of the input. There are many algorithms for solving sorting algorithms For example of bubble sort 8, 25,9,3,6 (networks).A sorting network is an abstract mathematical model of a network of wires and comparator modules that is used to sort 8 8 8 3 3 a sequence of numbers. Each comparator connects two wires and sorts the values by outputting the smaller value to one wire and 25 25 9 9 3 8 6 6 the large to the other. A sorting network consists of two items comparators and wires .each wires carries with its values and each 9 25 3 9 6 8 comparator takes two wires as input and output. This independence of comparison sequences is useful for parallel 3 25 6 9 execution of the algorithms. -
Sorting Algorithm 1 Sorting Algorithm
Sorting algorithm 1 Sorting algorithm In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order. The most-used orders are numerical order and lexicographical order. Efficient sorting is important for optimizing the use of other algorithms (such as search and merge algorithms) that require sorted lists to work correctly; it is also often useful for canonicalizing data and for producing human-readable output. More formally, the output must satisfy two conditions: 1. The output is in nondecreasing order (each element is no smaller than the previous element according to the desired total order); 2. The output is a permutation, or reordering, of the input. Since the dawn of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. For example, bubble sort was analyzed as early as 1956.[1] Although many consider it a solved problem, useful new sorting algorithms are still being invented (for example, library sort was first published in 2004). Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide and conquer algorithms, data structures, randomized algorithms, best, worst and average case analysis, time-space tradeoffs, and lower bounds. Classification Sorting algorithms used in computer science are often classified by: • Computational complexity (worst, average and best behaviour) of element comparisons in terms of the size of the list . For typical sorting algorithms good behavior is and bad behavior is . -
I. Sorting Networks Thomas Sauerwald
I. Sorting Networks Thomas Sauerwald Easter 2015 Outline Outline of this Course Introduction to Sorting Networks Batcher’s Sorting Network Counting Networks I. Sorting Networks Outline of this Course 2 Closely follow the book and use the same numberring of theorems/lemmas etc. I. Sorting Networks (Sorting, Counting, Load Balancing) II. Matrix Multiplication (Serial and Parallel) III. Linear Programming (Formulating, Applying and Solving) IV. Approximation Algorithms: Covering Problems V. Approximation Algorithms via Exact Algorithms VI. Approximation Algorithms: Travelling Salesman Problem VII. Approximation Algorithms: Randomisation and Rounding VIII. Approximation Algorithms: MAX-CUT Problem (Tentative) List of Topics Algorithms (I, II) Complexity Theory Advanced Algorithms I. Sorting Networks Outline of this Course 3 Closely follow the book and use the same numberring of theorems/lemmas etc. (Tentative) List of Topics Algorithms (I, II) Complexity Theory Advanced Algorithms I. Sorting Networks (Sorting, Counting, Load Balancing) II. Matrix Multiplication (Serial and Parallel) III. Linear Programming (Formulating, Applying and Solving) IV. Approximation Algorithms: Covering Problems V. Approximation Algorithms via Exact Algorithms VI. Approximation Algorithms: Travelling Salesman Problem VII. Approximation Algorithms: Randomisation and Rounding VIII. Approximation Algorithms: MAX-CUT Problem I. Sorting Networks Outline of this Course 3 (Tentative) List of Topics Algorithms (I, II) Complexity Theory Advanced Algorithms I. Sorting Networks (Sorting, Counting, Load Balancing) II. Matrix Multiplication (Serial and Parallel) III. Linear Programming (Formulating, Applying and Solving) IV. Approximation Algorithms: Covering Problems V. Approximation Algorithms via Exact Algorithms VI. Approximation Algorithms: Travelling Salesman Problem VII. Approximation Algorithms: Randomisation and Rounding VIII. Approximation Algorithms: MAX-CUT Problem Closely follow the book and use the same numberring of theorems/lemmas etc. -
Adaptive Bitonic Sorting
Encyclopedia of Parallel Computing “00101” — 2011/4/16 — 13:39 — Page 1 — #2 A One of the main di7erences between “regular” bitonic Adaptive Bitonic Sorting sorting and adaptive bitonic sorting is that regular bitonic sorting is data-independent, while adaptive G"#$%&' Z"()*"++ bitonic sorting is data-dependent (hence the name). Clausthal University, Clausthal-Zellerfeld, Germany As a consequence, adaptive bitonic sorting cannot be implemented as a sorting network, but only on archi- Definition tectures that o7er some kind of 9ow control. Nonethe- Adaptive bitonic sorting is a sorting algorithm suitable less, it is convenient to derive the method of adaptive for implementation on EREW parallel architectures. bitonic sorting from bitonic sorting. Similar to bitonic sorting, it is based on merging, which Sorting networks have a long history in computer is recursively applied to obtain a sorted sequence. In science research (see the comprehensive survey []). contrast to bitonic sorting, it is data-dependent. Adap- One reason is that sorting networks are a convenient tive bitonic merging can be performed in O n parallel p way to describe parallel sorting algorithms on CREW- time, p being the number of processors, and executes ! " PRAMs or even EREW-PRAMs (which is also called only O n operations in total. Consequently, adaptive n log n PRAC for “parallel random access computer”). bitonic sorting can be performed in O time, ( ) p In the following, let n denote the number of keys which is optimal. So, one of its advantages is that it exe- ! " to be sorted, and p the number of processors. For the cutes a factor of O log n less operations than bitonic sake of clarity, n will always be assumed to be a power sorting. -
Finalabc.Pdf
A. Department goals and objectives are linked to the university and college mission and strategic priorities, and to their strategy for improving their position within the discipline. (1 page maximum) 1. What is the department’s mission and is it clearly aligned with the university and college mission and direction? The department strives to offer quality undergraduate and graduate courses / programs; places a high priority on quality research and effective teaching; seeks to attract highly- qualified students; and strives to attract and nurture high-caliber faculty. This mission is consistent with university goals of ensuring student success, enhancing academic excellence, expanding breakthrough research, and developing / recognizing our people. 2. How does the department’s mission relate to curriculum; enrollments; faculty teaching; research/professional/creative activity and outreach? Is it aligned with the college’s strategic priorities? The departmental mission aligns with university and college strategic priorities, although the department is now in financial jeopardy under KSU’s new RCM budget model due to developmental growth in faculty numbers under state direction to grow a doctoral program. 3. How does the department contribute to university-wide curricular needs through general education and service instruction? The department was limited to a single Liberal Education Course (CS 10051 Introduction to Computer Science), but may have an opportunity to offer more courses under the new Kent Core curriculum. However, unlike many universities, KSU does not have a university-wide computing requirement, and does not have a large number of engineering majors taking CS courses. 4. How does the department promote diversity? The department has an active NSF S-STEM grant for broadening participation, and a diverse set of faculty, two of whom are women, and outreach activities to women and other minority students in computing. -
Evaluation of Sorting Algorithms, Mathematical and Empirical Analysis of Sorting Algorithms
International Journal of Scientific & Engineering Research Volume 8, Issue 5, May-2017 86 ISSN 2229-5518 Evaluation of Sorting Algorithms, Mathematical and Empirical Analysis of sorting Algorithms Sapram Choudaiah P Chandu Chowdary M Kavitha ABSTRACT:Sorting is an important data structure in many real life applications. A number of sorting algorithms are in existence till date. This paper continues the earlier thought of evolutionary study of sorting problem and sorting algorithms concluded with the chronological list of early pioneers of sorting problem or algorithms. Latter in the study graphical method has been used to present an evolution of sorting problem and sorting algorithm on the time line. An extensive analysis has been done compared with the traditional mathematical methods of ―Bubble Sort, Selection Sort, Insertion Sort, Merge Sort, Quick Sort. Observations have been obtained on comparing with the existing approaches of All Sorts. An “Empirical Analysis” consists of rigorous complexity analysis by various sorting algorithms, in which comparison and real swapping of all the variables are calculatedAll algorithms were tested on random data of various ranges from small to large. It is an attempt to compare the performance of various sorting algorithm, with the aim of comparing their speed when sorting an integer inputs.The empirical data obtained by using the program reveals that Quick sort algorithm is fastest and Bubble sort is slowest. Keywords: Bubble Sort, Insertion sort, Quick Sort, Merge Sort, Selection Sort, Heap Sort,CPU Time. Introduction In spite of plentiful literature and research in more dimension to student for thinking4. Whereas, sorting algorithmic domain there is mess found in this thinking become a mark of respect to all our documentation as far as credential concern2. -
Bitonic Sort and Quick Sort
Assignment of bachelor’s thesis Title: Development of parallel sorting algorithms for GPU Student: Xuan Thang Nguyen Supervisor: Ing. Tomáš Oberhuber, Ph.D. Study program: Informatics Branch / specialization: Computer Science Department: Department of Theoretical Computer Science Validity: until the end of summer semester 2021/2022 Instructions 1. Study the basics of programming GPU using CUDA. 2. Learn the fundamentals of the development of parallel algorithms with TNL library (www.tnl- project.org). 3. Learn and understand parallel sorting algorithms, namely bitonic sort and quick sort. 4. Implement both algorithms into TNL library to run on CPU and GPU. 5. Implement unit tests for testing correctness of the implemented algorithms. 6. Perform measurement of speed-up compared to sorting algorithms in the STL library and GPU implementation [1]. [1] https://github.com/davors/gpu-sorting Electronically approved by doc. Ing. Jan Janoušek, Ph.D. on 30 November 2020 in Prague. Bachelor’s thesis Development of parallel sorting algorithms for GPU Nguyen Xuan Thang Department of Theoretical Computer Science Supervisor: Ing. Tomáš Oberhuber, Ph.D. May 13, 2021 Acknowledgements I would like to thank my supervisor Ing. Tomáš Oberhuber, Ph.D. for his sup- port, guidance and advices throughout the whole time of creating this thesis. My gratitude also goes to my family that helped me during these hard times. Declaration I hereby declare that the presented thesis is my own work and that I have cited all sources of information in accordance with the Guideline for adhering to ethical principles when elaborating an academic final thesis. I acknowledge that my thesis is subject to the rights and obligations stip- ulated by the Act No. -
A Single SMC Sampler on MPI That Outperforms a Single MCMC Sampler
ASINGLE SMC SAMPLER ON MPI THAT OUTPERFORMS A SINGLE MCMC SAMPLER Alessandro Varsi Lykourgos Kekempanos Department of Electrical Engineering and Electronics Department of Electrical Engineering and Electronics University of Liverpool University of Liverpool Liverpool, L69 3GJ, UK Liverpool, L69 3GJ, UK [email protected] [email protected] Jeyarajan Thiyagalingam Simon Maskell Scientific Computing Department Department of Electrical Engineering and Electronics Rutherford Appleton Laboratory, STFC University of Liverpool Didcot, Oxfordshire, OX11 0QX, UK Liverpool, L69 3GJ, UK [email protected] [email protected] ABSTRACT Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms which are primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Single instances of MCMC methods are widely considered hard to parallelise in a problem-agnostic fashion and hence, unsuitable to meet both constraints of high accuracy and high throughput. Se- quential Monte Carlo (SMC) Samplers can address the same problem, but are parallelisable: they share with Particle Filters the same key tasks and bottleneck. Although a rich literature already exists on MCMC methods, SMC Samplers are relatively underexplored, such that no parallel im- plementation is currently available. In this paper, we first propose a parallel MPI version of the SMC Sampler, including an optimised implementation of the bottleneck, and then compare it with single-core Metropolis-Hastings. The goal is to show that SMC Samplers may be a promising alternative to MCMC methods with high potential for future improvements. We demonstrate that a basic SMC Sampler with 512 cores is up to 85 times faster or up to 8 times more accurate than Metropolis-Hastings. -
Sorting Algorithm 1 Sorting Algorithm
Sorting algorithm 1 Sorting algorithm A sorting algorithm is an algorithm that puts elements of a list in a certain order. The most-used orders are numerical order and lexicographical order. Efficient sorting is important for optimizing the use of other algorithms (such as search and merge algorithms) which require input data to be in sorted lists; it is also often useful for canonicalizing data and for producing human-readable output. More formally, the output must satisfy two conditions: 1. The output is in nondecreasing order (each element is no smaller than the previous element according to the desired total order); 2. The output is a permutation (reordering) of the input. Since the dawn of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. For example, bubble sort was analyzed as early as 1956.[1] Although many consider it a solved problem, useful new sorting algorithms are still being invented (for example, library sort was first published in 2006). Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide and conquer algorithms, data structures, randomized algorithms, best, worst and average case analysis, time-space tradeoffs, and upper and lower bounds. Classification Sorting algorithms are often classified by: • Computational complexity (worst, average and best behavior) of element comparisons in terms of the size of the list (n). For typical serial sorting algorithms good behavior is O(n log n), with parallel sort in O(log2 n), and bad behavior is O(n2). -
36 Algorithms.Txt 4/4/2010 Zhan and Noon Tested Algorithms For
36_Algorithms.txt 4/4/2010 Zhan and Noon tested algorithms for solving this problem, finding approximate or double bucket modifications to one algorithm and Pallattino's algorithm with two queues were fastest on actual data. Johnson's algorithm solves this problem in the sparse case faster than the cubic Floyd's algorithm, both of which solve this for all pairs. Another approach uses dynamic programming, and checks all edges n times; that algorithm also detects negative cost cycles, and is named for Bellman and Ford. A Fibonacci heap is used to speed up a greedy approach, which works only for positive-weight edges, while if an admissible heuristic is available, the A* algorithm can be used. For 10 points, identify this problem in graph theory, most famously solved by Dijkstra's algorithm, which asks for a fast route between two nodes. Answer: shortest path algorithms [accept with any of the following modifying the answer: all-pairs, single-source, or single-source single-destination] Along with a binary search tree, one of these structures is used to store future beach-line-changing events in Fortune's algorithm for generating Voronoi diagrams. The ROAM algorithm uses a pair of these data structures to store triangles that can be either split or merged. A meldable heap is a version of this structure implemented using a binomial heap, which gives it a "merge" operation, and the “fringe” structure in the A* algorithm is one of these. They're used on network routing protocols to ensure real-time traffic is forwarded first, and they optionally implement the PeekAtNext operation.