Performance Improvement for Multi-Key Quick Sort Using Kepler Gpus
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An Efficient Evolutionary Algorithm for Solving Incrementally Structured
An Efficient Evolutionary Algorithm for Solving Incrementally Structured Problems Jason Ansel Maciej Pacula Saman Amarasinghe Una-May O'Reilly MIT - CSAIL July 14, 2011 Jason Ansel (MIT) PetaBricks July 14, 2011 1 / 30 Our goal is to make programs run faster We use evolutionary algorithms to search for faster programs The PetaBricks language defines search spaces of algorithmic choices Who are we? I do research in programming languages (PL) and compilers The PetaBricks language is a collaboration between: A PL / compiler research group A evolutionary algorithms research group A applied mathematics research group Jason Ansel (MIT) PetaBricks July 14, 2011 2 / 30 The PetaBricks language defines search spaces of algorithmic choices Who are we? I do research in programming languages (PL) and compilers The PetaBricks language is a collaboration between: A PL / compiler research group A evolutionary algorithms research group A applied mathematics research group Our goal is to make programs run faster We use evolutionary algorithms to search for faster programs Jason Ansel (MIT) PetaBricks July 14, 2011 2 / 30 Who are we? I do research in programming languages (PL) and compilers The PetaBricks language is a collaboration between: A PL / compiler research group A evolutionary algorithms research group A applied mathematics research group Our goal is to make programs run faster We use evolutionary algorithms to search for faster programs The PetaBricks language defines search spaces of algorithmic choices Jason Ansel (MIT) PetaBricks July 14, 2011 -
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 . -
Fast Parallel GPU-Sorting Using a Hybrid Algorithm
Fast Parallel GPU-Sorting Using a Hybrid Algorithm Erik Sintorn Ulf Assarsson Department of Computer Science and Engineering Department of Computer Science and Engineering Chalmers University Of Technology Chalmers University Of Technology Gothenburg, Sweden Gothenburg, Sweden Email: [email protected] Email: uffe at chalmers dot se Abstract— This paper presents an algorithm for fast sorting of that supports scattered writing. The GPU-sorting algorithms large lists using modern GPUs. The method achieves high speed are highly bandwidth-limited, which is illustrated for instance by efficiently utilizing the parallelism of the GPU throughout the by the fact that sorting of 8-bit values [10] are nearly four whole algorithm. Initially, a parallel bucketsort splits the list into enough sublists then to be sorted in parallel using merge-sort. The times faster than for 32-bit values [2]. To improve the speed of parallel bucketsort, implemented in NVIDIA’s CUDA, utilizes the memory reads, we therefore design a vector-based mergesort, synchronization mechanisms, such as atomic increment, that is using CUDA and log n render passes, to work on four 32- available on modern GPUs. The mergesort requires scattered bit floats simultaneously, resulting in a nearly 4 times speed writing, which is exposed by CUDA and ATI’s Data Parallel improvement compared to merge-sorting on single floats. The Virtual Machine[1]. For lists with more than 512k elements, the algorithm performs better than the bitonic sort algorithms, which Vector-Mergesort of two four-float vectors is achieved by using have been considered to be the fastest for GPU sorting, and is a custom designed parallel compare-and-swap algorithm, on more than twice as fast for 8M elements. -
How to Sort out Your Life in O(N) Time
How to sort out your life in O(n) time arel Číže @kaja47K funkcionaklne.cz I said, "Kiss me, you're beautiful - These are truly the last days" Godspeed You! Black Emperor, The Dead Flag Blues Everyone, deep in their hearts, is waiting for the end of the world to come. Haruki Murakami, 1Q84 ... Free lunch 1965 – 2022 Cramming More Components onto Integrated Circuits http://www.cs.utexas.edu/~fussell/courses/cs352h/papers/moore.pdf He pays his staff in junk. William S. Burroughs, Naked Lunch Sorting? quicksort and chill HS 1964 QS 1959 MS 1945 RS 1887 quicksort, mergesort, heapsort, radix sort, multi- way merge sort, samplesort, insertion sort, selection sort, library sort, counting sort, bucketsort, bitonic merge sort, Batcher odd-even sort, odd–even transposition sort, radix quick sort, radix merge sort*, burst sort binary search tree, B-tree, R-tree, VP tree, trie, log-structured merge tree, skip list, YOLO tree* vs. hashing Robin Hood hashing https://cs.uwaterloo.ca/research/tr/1986/CS-86-14.pdf xs.sorted.take(k) (take (sort xs) k) qsort(lotOfIntegers) It may be the wrong decision, but fuck it, it's mine. (Mark Z. Danielewski, House of Leaves) I tell you, my man, this is the American Dream in action! We’d be fools not to ride this strange torpedo all the way out to the end. (HST, FALILV) Linear time sorting? I owe the discovery of Uqbar to the conjunction of a mirror and an Encyclopedia. (Jorge Luis Borges, Tlön, Uqbar, Orbis Tertius) Sorting out graph processing https://github.com/frankmcsherry/blog/blob/master/posts/2015-08-15.md Radix Sort Revisited http://www.codercorner.com/RadixSortRevisited.htm Sketchy radix sort https://github.com/kaja47/sketches (thinking|drinking|WTF)* I know they accuse me of arrogance, and perhaps misanthropy, and perhaps of madness. -
GPU Sample Sort We Should Mention That Hybrid Sort [15] and Bbsort [4] Involve a Distribution Phase Assuming That the Keys Are Uniformly Distributed
GPU Sample Sort Nikolaj Leischner∗ Vitaly Osipov† Peter Sanders‡ Abstract In this paper, we present the design of a sample sort algorithm for manycore GPUs. Despite being one of the most efficient comparison-based sorting algorithms for distributed memory architectures its performance on GPUs was previously unknown. For uniformly distributed keys our sample sort is at least 25% and on average 68% faster than the best comparison-based sorting algorithm, GPU Thrust merge sort, and on average more than 2 times faster than GPU quicksort. Moreover, for 64-bit integer keys it is at least 63% and on average 2 times faster than the highly optimized GPU Thrust radix sort that directly manipulates the binary representation of keys. Our implementation is robust to different distributions and entropy levels of keys and scales almost linearly with the input size. These results indicate that multi-way techniques in general and sample sort in particular achieve substantially better performance than two-way merge sort and quicksort. 1 Introduction Sorting is one of the most widely researched computational problems in computer science. It is an essential building block for numerous algorithms, whose performance depends on the efficiency of sorting. It is also an internal primitive utilized by database operations, and therefore, any applica- tion that uses a database may benefit from an efficient sorting algorithm. Geographic information systems, computational biology, and search engines are further fields that involve sorting. Hence, it is of utmost importance to provide efficient sort primitives for emerging architectures, which arXiv:0909.5649v1 [cs.DS] 30 Sep 2009 exploit architectural attributes, such as increased parallelism that were not available before. -
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). -
A Comparative Study of Sorting Algorithms with FPGA Acceleration by High Level Synthesis
A Comparative Study of Sorting Algorithms with FPGA Acceleration by High Level Synthesis Yomna Ben Jmaa1,2, Rabie Ben Atitallah2, David Duvivier2, Maher Ben Jemaa1 1 NIS University of Sfax, ReDCAD, Tunisia 2 Polytechnical University Hauts-de-France, France [email protected], fRabie.BenAtitallah, [email protected], [email protected] Abstract. Nowadays, sorting is an important operation the risk of accidents, the traffic jams and pollution. for several real-time embedded applications. It is one Also, ITS improve the transport efficiency, safety of the most commonly studied problems in computer and security of passengers. They are used in science. It can be considered as an advantage for various domains such as railways, avionics and some applications such as avionic systems and decision automotive technology. At different steps, several support systems because these applications need a applications need to use sorting algorithms such sorting algorithm for their implementation. However, as decision support systems, path planning [6], sorting a big number of elements and/or real-time de- cision making need high processing speed. Therefore, scheduling and so on. accelerating sorting algorithms using FPGA can be an attractive solution. In this paper, we propose an efficient However, the complexity and the targeted hardware implementation for different sorting algorithms execution platform(s) are the main performance (BubbleSort, InsertionSort, SelectionSort, QuickSort, criteria for sorting algorithms. Different platforms HeapSort, ShellSort, MergeSort and TimSort) from such as CPU (single or multi-core), GPU (Graphics high-level descriptions in the zynq-7000 platform. In Processing Unit), FPGA (Field Programmable addition, we compare the performance of different Gate Array) [14] and heterogeneous architectures algorithms in terms of execution time, standard deviation can be used. -
Parallelization of Tim Sort Algorithm Using Mpi and Cuda
JOURNAL OF CRITICAL REVIEWS ISSN- 2394-5125 VOL 7, ISSUE 09, 2020 PARALLELIZATION OF TIM SORT ALGORITHM USING MPI AND CUDA Siva Thanagaraja1, Keshav Shanbhag2, Ashwath Rao B3[0000-0001-8528-1646], Shwetha Rai4[0000-0002-5714-2611], and N Gopalakrishna Kini5 Department of Computer Science & Engineering Manipal Institute Of Technology Manipal Academy Of Higher Education Manipal, Karnataka, India-576104 Abstract— Tim Sort is a sorting algorithm developed in 2002 by Tim Peters. It is one of the secure engineered algorithms, and its high-level principle includes the sequence S is divided into monotonic runs (i.e., non- increasing or non-decreasing subsequence of S), which should be sorted and should be combined pairwise according to some specific rules. To interpret and examine the merging strategy (meaning that the order in which merge and merge runs are performed) of Tim Sort, we have implemented it in MPI and CUDA environment. Finally, it can be seen the difference in the execution time between serial Tim Sort and parallel Tim sort run in O (n log n) time . Index Terms— Hybrid algorithm, Tim sort algorithm, Parallelization, Merge sort algorithm, Insertion sort algorithm. I. INTRODUCTION Sorting algorithm Tim Sort [1] was designed in 2002 by Tim Peters. It is a hybrid parallel sorting algorithm that combines two different sorting algorithms. This includes insertion sort and merge sort. This algorithm is an effective method for well-defined instructions. The algorithm is concealed as a finite list for evaluating Tim sort function. Starting from an initial state and its information the guidelines define a method that when execution continues through a limited number of next states. -
Automatic Algorithm Recognition Based on Programming Schemas and Beacons Aalto University
Department of Computer Science and Engineering Aalto- Ahmad Taherkhani Taherkhani Ahmad DD 17 Automatic Algorithm / 2013 2013 Recognition Based on Automatic Algorithm Recognition Based on Programming Schemas and Beacons and Beacons Schemas Programming on Based Recognition Algorithm Automatic Programming Schemas and Beacons A Supervised Machine Learning Classification Approach Ahmad Taherkhani 9HSTFMG*aejijc+ ISBN 978-952-60-4989-2 BUSINESS + ISBN 978-952-60-4990-8 (pdf) ECONOMY ISSN-L 1799-4934 ISSN 1799-4934 ART + ISSN 1799-4942 (pdf) DESIGN + ARCHITECTURE University Aalto Aalto University School of Science SCIENCE + Department of Computer Science and Engineering TECHNOLOGY www.aalto.fi CROSSOVER DOCTORAL DOCTORAL DISSERTATIONS DISSERTATIONS Aalto University publication series DOCTORAL DISSERTATIONS 17/2013 Automatic Algorithm Recognition Based on Programming Schemas and Beacons A Supervised Machine Learning Classification Approach Ahmad Taherkhani A doctoral dissertation completed for the degree of Doctor of Science (Technology) (Doctor of Philosophy) to be defended, with the permission of the Aalto University School of Science, at a public examination held at the lecture hall T2 of the school on the 8th of March 2013 at 12 noon. Aalto University School of Science Department of Computer Science and Engineering Learning + Technology Group Supervising professor Professor Lauri Malmi Thesis advisor D. Sc. (Tech) Ari Korhonen Preliminary examiners Professor Jorma Sajaniemi, University of Eastern Finland, Finland Dr. Colin Johnson, University of Kent, United Kingdom Opponent Professor Tapio Salakoski, University of Turku, Finland Aalto University publication series DOCTORAL DISSERTATIONS 17/2013 © Ahmad Taherkhani ISBN 978-952-60-4989-2 (printed) ISBN 978-952-60-4990-8 (pdf) ISSN-L 1799-4934 ISSN 1799-4934 (printed) ISSN 1799-4942 (pdf) http://urn.fi/URN:ISBN:978-952-60-4990-8 Unigrafia Oy Helsinki 2013 Finland Publication orders (printed book): The dissertation can be read at http://lib.tkk.fi/Diss/ Abstract Aalto University, P.O. -
PART III Basic Data Types
PART III Basic Data Types 186 Chapter 7 Using Numeric Types Two kinds of number representations, integer and floating point, are supported by C. The various integer types in C provide exact representations of the mathematical concept of “integer” but can represent values in only a limited range. The floating-point types in C are used to represent the mathematical type “real.” They can represent real numbers over a very large range of magnitudes, but each number generally is an approximation, using a limited number of decimal places of precision. In this chapter, we define and explain the integer and floating-point data types built into C and show how to write their literal forms and I/O formats. We discuss the range of values that can be stored in each type, how to perform reliable arithmetic computations with these values, what happens when a number is converted (or cast) from one type to another, and how to choose the proper data type for a problem. We would like to think of numbers as integer values, not as patterns of bits in memory. This is possible most of the time when working with C because the language lets us name the numbers and compute with them symbolically. Details such as the length (in bytes) of the number and the arrangement of bits in those bytes can be ignored most of the time. However, inside the computer, the numbers are just bit patterns. This becomes evident when conditions such as integer overflow occur and a “correct” formula produces a wrong and meaningless answer. -
Applied C and C++ Programming
Applied C and C++ Programming Alice E. Fischer David W. Eggert University of New Haven Michael J. Fischer Yale University August 2018 Copyright c 2018 by Alice E. Fischer, David W. Eggert, and Michael J. Fischer All rights reserved. This manuscript may be used freely by teachers and students in classes at the University of New Haven and at Yale University. Otherwise, no part of it may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the authors. 192 Part III Basic Data Types 193 Chapter 7 Using Numeric Types Two kinds of number representations, integer and floating point, are supported by C. The various integer types in C provide exact representations of the mathematical concept of \integer" but can represent values in only a limited range. The floating-point types in C are used to represent the mathematical type \real." They can represent real numbers over a very large range of magnitudes, but each number generally is an approximation, using a limited number of decimal places of precision. In this chapter, we define and explain the integer and floating-point data types built into C and show how to write their literal forms and I/O formats. We discuss the range of values that can be stored in each type, how to perform reliable arithmetic computations with these values, what happens when a number is converted (or cast) from one type to another, and how to choose the proper data type for a problem. -
An English-Persian Dictionary of Algorithms and Data Structures
An EnglishPersian Dictionary of Algorithms and Data Structures a a zarrabibasuacir ghodsisharifedu algorithm B A all pairs shortest path absolute p erformance guarantee b alphab et abstract data typ e alternating path accepting state alternating Turing machine d Ackermans function alternation d Ackermanns function amortized cost acyclic digraph amortized worst case acyclic directed graph ancestor d acyclic graph and adaptive heap sort ANSI b adaptivekdtree antichain adaptive sort antisymmetric addresscalculation sort approximation algorithm adjacencylist representation arc adjacencymatrix representation array array index adjacency list array merging adjacency matrix articulation p oint d adjacent articulation vertex d b admissible vertex assignmentproblem adversary asso ciation list algorithm asso ciative binary function asso ciative array binary GCD algorithm asymptotic b ound binary insertion sort asymptotic lower b ound binary priority queue asymptotic space complexity binary relation binary search asymptotic time complexity binary trie asymptotic upp er b ound c bingo sort asymptotically equal to bipartite graph asymptotically tightbound bipartite matching