DOCSLIB.ORG

A Comparative Study of Sorting Algorithms with FPGA Acceleration by High Level Synthesis

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
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. and resource utilization. From the experimental results, we show that the SelectionSort is 1.01-1.23 times faster Firstly, the FPGA is the most preferable platform than other algorithms when N < 64; Otherwise, TimSort is the best algorithm. for implementing the sorting process. Thus, industry uses frequently FPGAs for many real-time Keywords. FPGA, sorting algorithms, heterogeneous applications improve performance in terms of architecture CPU/FPGA, zynq platform. execution time and energy consumption [4, 5]. On the other hand, using an FPGA board allows to build complex applications which have a high 1 Introduction performance. These applications are being made by receiving a large number of available At present, Intelligent Transportation Systems programmable fabrics. They provide an imple- (ITS) is an advanced application combining en- mentation of massively-parallel architectures [5]. gineering transport, communication technologies The increase in the complexity of the applications and geographical information systems. These has led to high-level design methodologies[10]. systems [15] play a significant part in minimizing Hence, High-Level Synthesis (HLS) tools have Computación y Sistemas, Vol. 23, No. 1, 2019, pp. 213–230 ISSN 1405-5546 doi: 10.13053/CyS-23-1-2999 214 Yomna Ben Jmaa, Rabie Ben Atitallah, David Duvivier, Maher Ben Jemaa been developed to improve the productivity of is lower than an optimal parameter (OP) which FPGA-based designs. depends on the target architecture and the However, the first generation of HLS has failed sorting implementation; otherwise, MergeSort is to meet hardware designers’ expectations; some considered with integrating some other steps to reasons have facilated researchers to continue improve the execution time. producing powerful hardware devices. Among The main goal of our work is to create a new these reasons, we quote the sharp increase simulator which simulates the behavior of elements of silicon capability; recent conceptions tend to / components related to intelligent transportation employ heterogeneous Systems on Chips (SoCs) systems; In [2], the authors implemented an and accelerators. The use of behavioral designs execution model for a future test bench and in place of Register-Transfer-Level (RTL) designs simulation. However, they propose a new allows improving design productivity, reducing the hardware and software execution support for the time-to-market constraints, detaching the algorithm next generation of test and simulation system from architecture to provide a wide exploration for in the field of avionics. In [33], the authors implementing solutions [11]. From a high-level developed an efficient algorithm for helicopter path programming language (C / C ++), Xilinx created planning. They proposed different scheduling the vivado HLS [34] tool to generate hardware methods for the optimization of the process on accelerators. a real time high performance heterogeneous The sorting algorithm is an important process architecture CPU/FPGA. The authors in [25] for several real-time embedded applications. presented a new method of 3D path design There are many sorting algorithms [17] in the using the concept of “Dubins gliding symmetry literature such as BubbleSort, InsertionSort and conjecture“. This method has been integrated in SelectionSort which are simple to develop and to a real-time decisional system to solve the security realize, but they have a weak performance (time problem. complexity is O(n2)). Several researchers have In our research group, several researchers used MergeSort, HeapSort and QuickSort with proposed a new adaptive approach for 2D path O(nlog(n)) time complexity to resolve the restricted planning according to the density of obstacle performance of these algorithms [17]. On the one in a static environment. They improved this hand, HeapSort starts with the construction of a approach into a new method of 3D path planning heap for the data group. Hence, it is essential to with multi-criteria optimizing. The main objective remove the greatest element and to put it at the end of this work is to propose a different optimized of the partially-sorted table. Moreover, QuickSort hardware accelerated version of sorting algo- is very efficient in the partition phase for dividing rithms (BubbleSort, InsertionSort, SelectionSort, the table into two. However, the selection of the HeapSort, ShellSort, QuickSort, TimSort and value of the pivot is an important issue. On the MergeSort) from High-Level descriptions in avionic other hand, MergeSort gives a comparison of each applications. We use several optimization steps to element index, chooses the smallest element, puts obtain an efficient hardware implementation in two them in an array and merges two sorted arrays. different cases: software and hardware for different Furthermore, other sorting algorithms are vectors and permutations. improving the previous one. For example, The paper is structured as follows: Section ShellSort is an enhancement of the insertion II presents several studies of different sorting sort of algorithm. It divides the list into a algorithms using different platforms (CPU, GPU minimum number of sub-lists which are sorted and FPGA). Section III shows a design flow of with the insertion sort algorithm. Hybrid sorting our application. Section IV gives an overview algorithms emerged as a mixture between several of sorting algorithms. Section V describes our sorting algorithms. For example, Timsort combines architecture and a variety of optimizations of MergeSort and InsertionSort. These algorithms hardware implementation. Section VI shows choose the InsertionSort if the number of elements experimental results. We conclude in Section VII. Computación y Sistemas, Vol. 23, No. 1, 2019, pp. 213–230 ISSN 1405-5546 doi: 10.13053/CyS-23-1-2999 A Comparative215 Study of Sorting Algorithms with FPGA Acceleration by High Level Synthesis Table 1. Complexity of the sorting algorithms — According to the number of elements to be sorted, we choose the corresponding sorting Best Average Worst BubbleSort O(n) O(n2) O(n2) algorithms. For example, if the number of ele- InsertionSort O(n) O(n2) O(n2) ments is small, then InsertionSort is selected, 2 2 2 SelectionSort O(n ) O(n ) O(n ) otherwise; MergeSort is recommended. HeapSort O(n log(n)) O(n log(n)) O(n log(n)) ShellSort O(n log(n)) O(n log(n)2) O(n log(n)2) QuickSort O(n log(n)) O(n log(n)) O(n2) Zurek et al. [35] proposed two different hardware MergeSort O(n log(n)) O(n log(n)) O(n log(n)) TimSort O(n) O(n log(n)) O(n log(n)) implementation algorithms: the quick-merge parallel and the hybrid algorithm (parallel bitonic algorithm on the GPU + sequence MergeSort on 2 Background and Related Work CPU) using a framework openMP and CUDA. They compared two new implementations with a different number of elements. The obtained result Sorting is a common process and it is considered shows that multicore sorting algorithms are the as one of the well-known problems in the best scalable and the most efficient. The GPU computational world. To achieve this, several sorting algorithms, compared to a single core, are algorithms are available in different research up to four times faster than the optimized quick works. They can be organized in various ways: sort algorithm. The implemented hybrid algorithm (executed partially on CPU and GPU) is more — Depending on the algorithm time complexity, efficient than algorithms only run on the GPU Table I presents three different cases (best, (despite transfer delays) but a little slower than the average and worst) of the complexity for most efficient, quick-merge parallel CPU algorithm. several sorting algorithms. We can mention They showed that the hybrid algorithm is slower that QuickSort, HeapSort, MergeSort, timSort than the most efficient quick-merge parallel CPU have a best complexity of O(nlog(n)) in algorithm. average case. By contrast, the worst case Abirami et al. [1] presented an efficient hardware performance for the four algorithms is O(n2) implementation of the MergeSort algorithm with obtained by QuickSort. A simple pretest Designing Digital Circuits. They measured makes all algorithms in the best case to O(n) the efficiency, reliability and complexity of the complexity. MergeSort algorithm with a digital circuit.
Load more

Recommended publications
  • Secure Multi-Party Sorting and Applications
    Secure Multi-Party Sorting and Applications Kristján Valur Jónsson1, Gunnar Kreitz2, and Misbah Uddin2 1 Reykjavik University 2 KTH—Royal Institute of Technology Abstract. Sorting is among the most fundamental and well-studied problems within computer science and a core step of many algorithms. In this article, we consider the problem of constructing a secure multi-party computing (MPC) protocol for sorting, building on previous results in the field of sorting networks. Apart from the immediate uses for sorting, our protocol can be used as a building-block in more complex algorithms. We present a weighted set intersection algorithm, where each party inputs a set of weighted ele- ments and the output consists of the input elements with their weights summed. As a practical example, we apply our protocols in a network security setting for aggregation of security incident reports from multi- ple reporters, specifically to detect stealthy port scans in a distributed but privacy preserving manner. Both sorting and weighted set inter- section use O`n log2 n´ comparisons in O`log2 n´ rounds with practical constants. Our protocols can be built upon any secret sharing scheme supporting multiplication and addition. We have implemented and evaluated the performance of sorting on the Sharemind secure multi-party computa- tion platform, demonstrating the real-world performance of our proposed protocols. Keywords. Secure multi-party computation; Sorting; Aggregation; Co- operative anomaly detection 1 Introduction Intrusion Detection Systems (IDS) [16] are commonly used to detect anoma- lous and possibly malicious network traffic. Incidence reports and alerts from such systems are generally kept private, although much could be gained by co- operative sharing [30].
    [Show full text]
  • Batcher's Algorithm
    18.310 lecture notes Fall 2010 Batcher’s Algorithm Prof. Michel Goemans Perhaps the most restrictive version of the sorting problem requires not only no motion of the keys beyond compare-and-switches, but also that the plan of comparison-and-switches be fixed in advance. In each of the methods mentioned so far, the comparison to be made at any time often depends upon the result of previous comparisons. For example, in HeapSort, it appears at first glance that we are making only compare-and-switches between pairs of keys, but the comparisons we perform are not fixed in advance. Indeed when fixing a headless heap, we move either to the left child or to the right child depending on which child had the largest element; this is not fixed in advance. A sorting network is a fixed collection of comparison-switches, so that all comparisons and switches are between keys at locations that have been specified from the beginning. These comparisons are not dependent on what has happened before. The corresponding sorting algorithm is said to be non-adaptive. We will describe a simple recursive non-adaptive sorting procedure, named Batcher’s Algorithm after its discoverer. It is simple and elegant but has the disadvantage that it requires on the order of n(log n)2 comparisons. which is larger by a factor of the order of log n than the theoretical lower bound for comparison sorting. For a long time (ten years is a long time in this subject!) nobody knew if one could find a sorting network better than this one.
    [Show full text]
  • Sorting Algorithms Correcness, Complexity and Other Properties
    Sorting Algorithms Correcness, Complexity and other Properties Joshua Knowles School of Computer Science The University of Manchester COMP26912 - Week 9 LF17, April 1 2011 The Importance of Sorting Important because • Fundamental to organizing data • Principles of good algorithm design (correctness and efficiency) can be appreciated in the methods developed for this simple (to state) task. Sorting Algorithms 2 LF17, April 1 2011 Every algorithms book has a large section on Sorting... Sorting Algorithms 3 LF17, April 1 2011 ...On the Other Hand • Progress in computer speed and memory has reduced the practical importance of (further developments in) sorting • quicksort() is often an adequate answer in many applications However, you still need to know your way (a little) around the the key sorting algorithms Sorting Algorithms 4 LF17, April 1 2011 Overview What you should learn about sorting (what is examinable) • Definition of sorting. Correctness of sorting algorithms • How the following work: Bubble sort, Insertion sort, Selection sort, Quicksort, Merge sort, Heap sort, Bucket sort, Radix sort • Main properties of those algorithms • How to reason about complexity — worst case and special cases Covered in: the course book; labs; this lecture; wikipedia; wider reading Sorting Algorithms 5 LF17, April 1 2011 Relevant Pages of the Course Book Selection sort: 97 (very short description only) Insertion sort: 98 (very short) Merge sort: 219–224 (pages on multi-way merge not needed) Heap sort: 100–106 and 107–111 Quicksort: 234–238 Bucket sort: 241–242 Radix sort: 242–243 Lower bound on sorting 239–240 Practical issues, 244 Some of the exercise on pp.
    [Show full text]
  • Sorting and Asymptotic Complexity
    SORTING AND ASYMPTOTIC COMPLEXITY Lecture 14 CS2110 – Fall 2013 Reading and Homework 2 Texbook, chapter 8 (general concepts) and 9 (MergeSort, QuickSort) Thought question: Cloud computing systems sometimes sort data sets with hundreds of billions of items – far too much to fit in any one computer. So they use multiple computers to sort the data. Suppose you had N computers and each has room for D items, and you have a data set with N*D/2 items to sort. How could you sort the data? Assume the data is initially in a big file, and you’ll need to read the file, sort the data, then write a new file in sorted order. InsertionSort 3 //sort a[], an array of int Worst-case: O(n2) for (int i = 1; i < a.length; i++) { (reverse-sorted input) // Push a[i] down to its sorted position Best-case: O(n) // in a[0..i] (sorted input) int temp = a[i]; Expected case: O(n2) int k; for (k = i; 0 < k && temp < a[k–1]; k– –) . Expected number of inversions: n(n–1)/4 a[k] = a[k–1]; a[k] = temp; } Many people sort cards this way Invariant of main loop: a[0..i-1] is sorted Works especially well when input is nearly sorted SelectionSort 4 //sort a[], an array of int Another common way for for (int i = 1; i < a.length; i++) { people to sort cards int m= index of minimum of a[i..]; Runtime Swap b[i] and b[m]; . Worst-case O(n2) } . Best-case O(n2) .
    [Show full text]
  • 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.
    [Show full text]
  • Selected Sorting Algorithms
    Selected Sorting Algorithms CS 165: Project in Algorithms and Data Structures Michael T. Goodrich Some slides are from J. Miller, CSE 373, U. Washington Why Sorting? • Practical application – People by last name – Countries by population – Search engine results by relevance • Fundamental to other algorithms • Different algorithms have different asymptotic and constant-factor trade-offs – No single ‘best’ sort for all scenarios – Knowing one way to sort just isn’t enough • Many to approaches to sorting which can be used for other problems 2 Problem statement There are n comparable elements in an array and we want to rearrange them to be in increasing order Pre: – An array A of data records – A value in each data record – A comparison function • <, =, >, compareTo Post: – For each distinct position i and j of A, if i < j then A[i] ≤ A[j] – A has all the same data it started with 3 Insertion sort • insertion sort: orders a list of values by repetitively inserting a particular value into a sorted subset of the list • more specifically: – consider the first item to be a sorted sublist of length 1 – insert the second item into the sorted sublist, shifting the first item if needed – insert the third item into the sorted sublist, shifting the other items as needed – repeat until all values have been inserted into their proper positions 4 Insertion sort • Simple sorting algorithm. – n-1 passes over the array – At the end of pass i, the elements that occupied A[0]…A[i] originally are still in those spots and in sorted order.
    [Show full text]
  • Advanced Topics in Sorting
    Advanced Topics in Sorting complexity system sorts duplicate keys comparators 1 complexity system sorts duplicate keys comparators 2 Complexity of sorting Computational complexity. Framework to study efficiency of algorithms for solving a particular problem X. Machine model. Focus on fundamental operations. Upper bound. Cost guarantee provided by some algorithm for X. Lower bound. Proven limit on cost guarantee of any algorithm for X. Optimal algorithm. Algorithm with best cost guarantee for X. lower bound ~ upper bound Example: sorting. • Machine model = # comparisons access information only through compares • Upper bound = N lg N from mergesort. • Lower bound ? 3 Decision Tree a < b yes no code between comparisons (e.g., sequence of exchanges) b < c a < c yes no yes no a b c b a c a < c b < c yes no yes no a c b c a b b c a c b a 4 Comparison-based lower bound for sorting Theorem. Any comparison based sorting algorithm must use more than N lg N - 1.44 N comparisons in the worst-case. Pf. Assume input consists of N distinct values a through a . • 1 N • Worst case dictated by tree height h. N ! different orderings. • • (At least) one leaf corresponds to each ordering. Binary tree with N ! leaves cannot have height less than lg (N!) • h lg N! lg (N / e) N Stirling's formula = N lg N - N lg e N lg N - 1.44 N 5 Complexity of sorting Upper bound. Cost guarantee provided by some algorithm for X. Lower bound. Proven limit on cost guarantee of any algorithm for X.
    [Show full text]
  • 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 .
    [Show full text]
  • Faster Shellsort Sequences: a Genetic Algorithm Application
    Faster Shellsort Sequences: A Genetic Algorithm Application Richard Simpson Shashidhar Yachavaram [email protected] [email protected] Department of Computer Science Midwestern State University 3410 Taft, Wichita Falls, TX 76308 Phone: (940) 397-4191 Fax: (940) 397-4442 Abstract complex problems that resist normal research approaches. This paper concerns itself with the application of Genetic The recent popularity of genetic algorithms (GA's) and Algorithms to the problem of finding new, more efficient their application to a wide variety of problems is a result of Shellsort sequences. Using comparison counts as the main their ease of implementation and flexibility. Evolutionary criteria for quality, several new sequences have been techniques are often applied to optimization and related discovered that sort one megabyte files more efficiently than search problems where the fitness of a potential result is those presently known. easily established. Problems of this type are generally very difficult and often NP-Hard, so the ability to find a reasonable This paper provides a brief introduction to genetic solution to these problems within an acceptable time algorithms, a review of research on the Shellsort algorithm, constraint is clearly desirable. and concludes with a description of the GA approach and the associated results. One such problem that has been researched thoroughly is the search for Shellsort sequences. The attributes of this 2. Genetic Algorithms problem make it a prime target for the application of genetic algorithms. Noting this, the authors have designed a GA that John Holland developed the technique of GA's in the efficiently searches for Shellsort sequences that are top 1960's.
    [Show full text]
  • Arxiv:1812.03318V1 [Cs.SE] 8 Dec 2018 Rived from Merge Sort and Insertion Sort, Designed to Work Well on Many Kinds of Real-World Data
    A Verified Timsort C Implementation in Isabelle/HOL Yu Zhang1, Yongwang Zhao1 , and David Sanan2 1 School of Computer Science and Engineering, Beihang University, Beijing, China [email protected] 2 School of Computer Science and Engineering, Nanyang Technological University, Singapore Abstract. Formal verification of traditional algorithms are of great significance due to their wide application in state-of-the-art software. Timsort is a complicated and hybrid stable sorting algorithm, derived from merge sort and insertion sort. Although Timsort implementation in OpenJDK has been formally verified, there is still not a standard and formally verified Timsort implementation in C programming language. This paper studies Timsort implementation and its formal verification using a generic imperative language - Simpl in Isabelle/HOL. Then, we manually generate an C implementation of Timsort from the verified Simpl specification. Due to the C-like concrete syntax of Simpl, the code generation is straightforward. The C implementation has also been tested by a set of random test cases. Keywords: Program Verification · Timsort · Isabelle/HOL 1 Introduction Formal verification has been considered as a promising way to the reliability of programs. With development of verification tools, it is possible to perform fully formal verification of large and complex programs in recent years [2,3]. Formal verification of traditional algorithms are of great significance due to their wide application in state-of-the-art software. The goal of this paper is the functional verification of sorting algorithms as well as generation of C source code. We investigated Timsort algorithm which is a hybrid stable sorting algorithm, de- arXiv:1812.03318v1 [cs.SE] 8 Dec 2018 rived from merge sort and insertion sort, designed to work well on many kinds of real-world data.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]