CSE 373: Floyd's Buildheap Algorithm
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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 . -
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. -
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). -
STUDY of NON-COMPARISON SORTING ALGORITHMS By
STUDY OF NON-COMPARISON SORTING ALGORITHMS By ZHIMINMA Bachelor of Science Beijing University of Aeronautics & Astronauntics Beijing, P.R.China 1990 Suhmitted to the Faculty of the Graduate College of the Oklahoma State University In partial fulfillment of the requirements for the Degree of MASTER OF SCIENCE May, 2000 • STUDY OF NON-COMPARISON SORTING ALGORITHMS Thesis Approved: Uay11R.) 13. foudi. Dean of the Graduate College II PREFACE The primary purpose of this project is to compare two new non-comparison sorting algorithms: Groupsort and Flashsort 1. To simplify discussion, we focus on the performance of these algorithms with integer data. First, we test Groupsort and Flashsort1 against bucket sort using uniformly distributed integer values with a number of different additional storage spaces and give run time performance curves. Then, we test Groupsort and Flashsortl against Quicksort using different distributed input data and give run time perfomance curves. Through the analysis of impact of run time, additional storage space, and data distribution, an optimal method is given to make each algonthm perform well. I sincerely thank my M.S. Committee - Drs. J. P. Chandler. G. L. Ikdnck, and B. E. Mayfield --- for guidance and support in the completion or this research. III ACKNOWLEDGMENTS I wish to express my sincere appreciation to my advisor, Dr. J. P. Chandler, for his intelligent supervision, constructive guidance, and inspiration, My sincere appreciation extends to my other committee members Dr. G. E. Hedrick, and Dr. B. E. Mayfield, whose guidance, assistance, and encouragement were also invaluable. 1would like to give my special appreciation to my parents Mr. -
Adaptive and Secured Resource Management in Distributed and Internet Systems
W&M ScholarWorks Dissertations, Theses, and Masters Projects Theses, Dissertations, & Master Projects 2002 Adaptive and secured resource management in distributed and Internet systems Li Xiao College of William & Mary - Arts & Sciences Follow this and additional works at: https://scholarworks.wm.edu/etd Part of the Computer Sciences Commons Recommended Citation Xiao, Li, "Adaptive and secured resource management in distributed and Internet systems" (2002). Dissertations, Theses, and Masters Projects. Paper 1539623406. https://dx.doi.org/doi:10.21220/s2-deqc-ew25 This Dissertation is brought to you for free and open access by the Theses, Dissertations, & Master Projects at W&M ScholarWorks. It has been accepted for inclusion in Dissertations, Theses, and Masters Projects by an authorized administrator of W&M ScholarWorks. For more information, please contact [email protected]. Reproduced with with permission permission of the of copyright the copyright owner. owner.Further reproductionFurther reproduction prohibited without prohibited permission. without permission. Adaptive and Secured Resource Management in Distributed and Internet Systems A Dissertation Presented to The Faculty of the Department of Computer Science The College of William & Mary in Virginia In Partial Fulfillment Of the Requirements for the Degree of Doctor of Philosophy by Li Xiao 2002 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPROVAL SHEET Tliis dissertation is submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy .JU Li Xiao Approved. July 2002 Thesis Advisor V)JjU^ 'I William L. Bvmun ' Phil Kearns c/C'-vX ^ A^ Robert E. Noonan Marc Slier Department of Physics Reproduced with permission of the copyright owner. -
Sorting Using Bitonic Network with CUDA
Sorting using BItonic netwoRk wIth CUDA Ranieri Baraglia Gabriele Capannini ISTI - CNR ISTI - CNR Via G. Moruzzi, 1 Via G. Moruzzi, 1 56124 Pisa, Italy 56124 Pisa, Italy [email protected] [email protected] Franco Maria Nardini Fabrizio Silvestri ISTI - CNR ISTI - CNR Via G. Moruzzi, 1 Via G. Moruzzi, 1 56124 Pisa, Italy 56124 Pisa, Italy [email protected] [email protected] ABSTRACT keep them up to date. Storage space must be used efficiently Novel \manycore" architectures, such as graphics processors, to store indexes, and documents. The indexing system must are high-parallel and high-performance shared-memory ar- process hundreds of gigabytes of data efficiently. Queries chitectures [7] born to solve specific problems such as the must be handled quickly, at a rate of hundreds to thousands graphical ones. Those architectures can be exploited to per second. All these services run on clusters of homoge- solve a wider range of problems by designing the related neous PCs. PCs in these clusters depends upon price, CPU algorithm for such architectures. We present a fast sorting speed, memory and disk size, heat output, and physical size algorithm implementing an efficient bitonic sorting network. [3]. Nowadays these characteristics can be find also in other This algorithm is highly suitable for information retrieval commodity hardware originally designed for specific graph- applications. Sorting is a fundamental and universal prob- ics computations. Many special processor architectures have lem in computer science. Even if sort has been extensively been proposed to exploit data parallelism for data intensive addressed by many research works, it still remains an inter- computations and graphics processors (GPUs) are one of esting challenge to make it faster by exploiting novel tech- those. -
Engineering Cache-Oblivious Sorting Algorithms
Engineering Cache-Oblivious Sorting Algorithms Master’s Thesis by Kristoffer Vinther June 2003 Abstract Modern computers are far more sophisticated than simple sequential programs can lead one to believe; instructions are not executed sequentially and in constant time. In particular, the memory of a modern computer is structured in a hierarchy of increasingly slower, cheaper, and larger storage. Accessing words in the lower, faster levels of this hierarchy can be done virtually immediately, but accessing the upper levels may cause delays of millions of processor cycles. Consequently, recent developments in algorithm design have had a focus on developing algorithms that sought to minimize accesses to the higher levels of the hierarchy. Much experimental work has been done showing that using these algorithms can lead to higher performing algorithms. However, these algorithms are designed and implemented with a very specific level in mind, making it infeasible to adapt them to multiple levels or use them efficiently on different architectures. To alleviate this, the notion of cache-oblivious algorithms was developed. The goal of a cache-oblivious algorithm is to be optimal in the use of the memory hierarchy, but without using specific knowledge of its structure. This automatically makes the algorithm efficient on all levels of the hierarchy and on all implementations of such hierarchies. The experimental work done with these types of algorithms remain sparse, however. In this thesis, we present a thorough theoretical and experimental analysis of known optimal cache-oblivious sorting algorithms. We develop our own simpler variants and present the first optimal sub-linear working space cache-oblivious sorting algorithm. -
Implementations of Randomized Sorting on Large Parallel Machines
Implementations of Randomized Sorting on Large Parallel Machines (Preliminary Version) William L. Hightower Jan F. Prins† John H. Reif‡ Elon College University of North Carolina Duke University Elon College NC 27244 Chapel Hill NC 27599-3175 Durham NC 27706 Abstract 1. Introduction Flashsort [RV83,86] and Samplesort [HC83] are Considerable effort has been made by the theoretical related parallel sorting algorithms proposed in the literature. community in the design of parallel algorithms with Both utilize a sophisticated randomized sampling technique excellent and sometimes optimal asymptotic efficiency. to form a splitter set, but Samplesort distributes the splitter However, the field has had less success in demonstrating the set to each processor while Flashsort uses splitter-directed utility of these algorithms by actual implementations. routing. Ideally, the analysis of parallel algorithms should proceed In this paper we present B-Flashsort, a new beyond asymptotic efficiency and be extended to the level of batched-routing variant of Flashsort designed to sort N>P implementations. In practice, this is difficult to do. values using P processors connected in a d-dimensional mesh and using constant space in addition to the input and For one thing, the relation between the asymptotic output. The key advantage of the Flashsort approach over complexity of an algorithm and the performance of an Samplesort is a decrease in memory requirements, by implementation can be considerably more complex for avoiding the broadcast of the splitter set to all processors. implementations of parallel algorithms than for sequential The practical advantage of B-Flashsort over Flashsort is that algorithms. For example, the number of processors or the it replaces pipelined splitter-directed routing with a set of amount of memory available to a processor in existing synchronous local communications and bounds recursion, machines can easily be reached well before the while still being demonstrably efficient. -
Engineering Burstsort: Toward Fast In-Place String Sorting
Engineering Burstsort: Toward Fast In-Place String Sorting RANJAN SINHA and ANTHONY WIRTH The University of Melbourne Burstsort is a trie-based string sorting algorithm that distributes strings into small buckets whose contents are then sorted in cache. This approach has earlier been demonstrated to be efficient on modern cache-based processors [Sinha & Zobel, JEA 2004]. In this article, we introduce improve- ments that reduce by a significant margin the memory requirement of Burstsort: It is now less than 1% greater than an in-place algorithm. These techniques can be applied to existing variants of Burstsort, as well as other string algorithms such as for string management. We redesigned the buckets, introducing sub-buckets and an index structure for them, which resulted in an order-of-magnitude space reduction. We also show the practicality of moving some fields from the trie nodes to the insertion point (for the next string pointer) in the bucket; this technique reduces memory usage of the trie nodes by one-third. Importantly, the trade-off for the reduction in memory use is only a very slight increase in the running time of Burstsort on real- world string collections. In addition, during the bucket-sorting phase, the string suffixes are copied to a small buffer to improve their spatial locality, lowering the running time of Burstsort by up to 30%. These memory usage enhancements have enabled the copy-based approach [Sinha et al., JEA 2006] to also reduce the memory usage with negligible impact on speed. 2.5 Categories and Subject Descriptors: E.1 [Data Structures]; E.5 [Files]: Sorting/Searching General Terms: Algorithms, Design, Experimentation, Performance Additional Key Words and Phrases: Sorting, algorithms, cache, experimental algorithms, string management, tries ACM Reference Format: Sinha, R. -
Sorting Using Bitonic Network with CUDA
Sorting using BItonic netwoRk wIth CUDA Ranieri Baraglia Gabriele Capannini ISTI - CNR ISTI - CNR Via G. Moruzzi, 1 Via G. Moruzzi, 1 56124 Pisa, Italy 56124 Pisa, Italy [email protected] [email protected] Franco Maria Nardini Fabrizio Silvestri ISTI - CNR ISTI - CNR Via G. Moruzzi, 1 Via G. Moruzzi, 1 56124 Pisa, Italy 56124 Pisa, Italy [email protected] [email protected] ABSTRACT keep them up to date. Storage space must be used efficiently Novel “manycore” architectures, such as graphics processors, to store indexes, and documents. The indexing system must are high-parallel and high-performance shared-memory ar- process hundreds of gigabytes of data efficiently. Queries chitectures [7] born to solve specific problems such as the must be handled quickly, at a rate of hundreds to thousands graphical ones. Those architectures can be exploited to per second. All these services run on clusters of homoge- solve a wider range of problems by designing the related neous PCs. PCs in these clusters depends upon price, CPU algorithm for such architectures. We present a fast sorting speed, memory and disk size, heat output, and physical size algorithm implementing an efficient bitonic sorting network. [3]. Nowadays these characteristics can be find also in other This algorithm is highly suitable for information retrieval commodity hardware originally designed for specific graph- applications. Sorting is a fundamental and universal prob- ics computations. Many special processor architectures have lem in computer science. Even if sort has been extensively been proposed to exploit data parallelism for data intensive addressed by many research works, it still remains an inter- computations and graphics processors (GPUs) are one of esting challenge to make it faster by exploiting novel tech- those. -
In Search of the Fastest Sorting Algorithm
In Search of the Fastest Sorting Algorithm Emmanuel Attard Cassar [email protected] Abstract: This paper explores in a chronological way the concepts, structures, and algorithms that programmers and computer scientists have tried out in their attempt to produce and improve the process of sorting. The measure of ‘fastness’ in this paper is mainly given in terms of the Big O notation. Keywords: sorting, algorithms orting is an extremely useful procedure in our information-laden society. Robert Sedgewick and Kevin Wayne have this to say: ‘In Sthe early days of computing, the common wisdom was that up to 30 per cent of all computing cycles was spent sorting. If that fraction is lower today, one likely reason is that sorting algorithms are relatively efficient, not that sorting has diminished in relative importance.’1 Many computer scientists consider sorting to be the most fundamental problem in the study of algorithms.2 In the literature, sorting is mentioned as far back as the seventh century BCE where the king of Assyria sorted clay tablets for the royal library according to their shape.3 1 R. Sedgewick, K. Wayne, Algorithms, 4th edn. (USA, 2011), Kindle Edition, Locations 4890-4892. 2 T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to Algorithms, 3rd edn. (USA, 2009), 148. 3 N. Akhter, M. Idrees, Furqan-ur-Rehman, ‘Sorting Algorithms – A Comparative Study’, International Journal of Computer Science and Information Security, Vol. 14, No. 12, (2016), 930. Symposia Melitensia Number 14 (2018) SYMPOSIA MELITENSIA NUMBER 14 (2018) Premise My considerations will be limited to algorithms on the standard von Neumann computer.