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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). -
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 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. -
Cache-Efficient String Sorting Using Copying
Cache-Efficient String Sorting Using Copying RANJAN SINHA and JUSTIN ZOBEL RMIT University and DAVID RING Palo Alto, CA Burstsort is a cache-oriented sorting technique that uses a dynamic trie to efficiently divide large sets of string keys into related subsets small enough to sort in cache. In our original burstsort, string keys sharing a common prefix were managed via a bucket of pointers represented as a list or array; this approach was found to be up to twice as fast as the previous best string sorts, mostly because of a sharp reduction in out-of-cache references. In this paper, we introduce C-burstsort, which copies the unexamined tail of each key to the bucket and discards the original key to improve data locality. On both Intel and PowerPC architectures, and on a wide range of string types, we show that sorting is typically twice as fast as our original burstsort and four to five times faster than multikey quicksort and previous radixsorts. A variant that copies both suffixes and record pointers to buckets, CP-burstsort, uses more memory, but provides stable sorting. In current computers, where performance is limited by memory access latencies, these new algorithms can dramatically reduce the time needed for internal sorting of large numbers of strings. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms]: Sorting; E.5 [Files]: Sorting; E.1 [Data Structures]: Trees; B.3.2 [Memory Structures]: Cache Memories; D.1.0 [Program- ming Techniques]: General General Terms: Algorithms, Design, Experimentation, Performance Additional Key Words and Phrases: Sorting, string management, cache, tries, algorthims, experi- mental algorithms 1. -
Efficient Trie-Based Sorting of Large Sets of Strings
Efficient Trie-Based Sorting of Large Sets of Strings Ranjan Sinha Justin Zobel School of Computer Science and Information Technology RMIT University, GPO Box 2476V, Melbourne 3001, Australia frsinha,[email protected] Abstract purpose methods (Bentley & Sedgewick 1998). Many of these methods are adaptations of radixsort. In Sorting is a fundamental algorithmic task. Many general- radixsorts, the items to be sorted are treated as se- purpose sorting algorithms have been developed, but efficiency quences of symbols drawn from a finite alphabet, and gains can be achieved by designing algorithms for specific kinds each symbol is represented in a fixed number of bits. of data, such as strings. In previous work we have shown that Traditional radixsort proceeds by assuming the items our burstsort, a trie-based algorithm for sorting strings, is for to consist of a fixed number of symbols and ordering large data sets more efficient than all previous algorithms for the items on the rightmost or least significant sym- this task. In this paper we re-evaluate some of the implemen- bol, then the next rightmost symbol, and so on. Thus tation details of burstsort, in particular the method for man- the final stage is to sort on the most significant sym- aging buckets held at leaves. We show that better choice of bol. However, such right-to-left approaches are not data structures further improves the efficiency, at a small ad- well-suited to variable-length strings. ditional cost in memory. For sets of around 30,000,000 strings, The newer radixsort algorithms are left-to-right or our improved burstsort is nearly twice as fast as the previous MSD (most significant digit first), commencing at the best sorting algorithm. -
LSDS-IR'09 7Th Workshop on Large-Scale Distributed Systems For
Claudio Lucchese Gleb Skobeltsyn Wai Gen Yee (Eds.) LSDS-IR’09 7th Workshop on Large-Scale Distributed Systems for Information Retrieval Workshop co-located with ACM SIGIR 2009 Boston, MA, USA, July 23, 2009 Proceedings Copyright c 2009 for the individual papers by the papers’ authors. Copying permitted for private and academic purposes. Re-publication of material from this volume requires permission by the copyright owners. Editors’ addresses: Claudio Lucchese Gleb Skobeltsyn Wai Gen Yee Istituto di Scienza e Tecnologie dell’Informazione Google Inc. Department of Computer Science Consiglio Nazionale delle Ricerche Illinois Institute of Technology Area della Ricerca di Pisa Via G. Moruzzi, 1 Brandschenkestrasse 110 10 W. 31st Street 56124 Pisa (PI) 8002 Zurich Chicago, IL 60616 Italy Switzerland USA [email protected] [email protected] [email protected] 7th Workshop on Large-Scale Distributed Systems for Information Retrieval (LSDS-IR’09) Preface The Web is continuously growing. Currently, it contains more than 20 billion pages (some sources suggest more than 100 billion), compared with fewer than 1 billion in 1998. Traditionally, Web-scale search engines employ large and highly replicated systems, operating on computer clusters in one or few data centers. Coping with the increasing number of user requests and indexable pages requires adding more resources. However, data centers cannot grow indefinitely. Scalability problems in Information Retrieval (IR) have to be addressed in the near future, and new distributed applications are likely to drive the way in which people use the Web. Distributed IR is the point in which these two directions converge. The 7th Large-Scale Distributed Systems Workshop (LSDS-IR’09), co-located with the 2009 ACM SIGIR Conference, provides a space for researchers to discuss these problems and to define new research directions in the area. -
Performance Improvement for Multi-Key Quick Sort Using Kepler Gpus
Performance Improvement for Multi-Key Quick Sort using Kepler GPUs Bharath Shamasundar, Amoolya Shetty Ananya Rao, Supreetha Shetty, Neelima Bayyapu Department of Computer Science and Engineering Department of Computer Science and Engineering NMAM Institute of Technology NMAM Institute of Technology Udupi, India Udupi, India {bharathbs294, amushetty93}@gmail.com {ananyaraoj, supreethashetty8}@gmail.com; [email protected] Abstract — This paper presents the performance programmers making it easily programmable. One improvement obtained by multi key quick sort on such programming API that has been introduced Kepler NVIDIA GPUs. Since Multi key quick sort by NVidia for parallel computing using GPUs is is a recursion based algorithm many of the the Compute Unified Device Architecture researchers have found it laborious to parallelize (CUDA) [2-3]. the algorithm on the multi and many core With every new version of the GPU architectures. A survey of imperative string sorting architecture, there is an increased possibility of algorithm and a robust perceptivity of the Kepler applications that can take advantage of this GPU architecture gave rise to an intriguing improvement. A sorting algorithm, based on rumination of matching the template of Multi key recursion that was previously considered quick sort with the dynamic parallelism feature offered by the Kepler based GPU’s. The CPU incapable of being parallelized in terms of parallel implementation of parallel multi key quick GPGPU is now ported onto the latest GPU sort gives 33 to 50 percentage of improvement and architecture that supports the framework of the 62 to 75 percentage of improvement when sorting algorithm is considered in this paper. compared to 8-bit and 16-bit parallel MSD radix Some research studies have provided a sort respectively.