Journal ArticleDOI
Cache-Oblivious Algorithms
TLDR
It is proved that an optimal cache-oblivious algorithm designed for two levels of memory is also optimal for multiple levels and that the assumption of optimal replacement in the ideal-cache model can be simulated efficiently by LRU replacement.Abstract:
This article presents asymptotically optimal algorithms for rectangular matrix transpose, fast Fourier transform (FFT), and sorting on computers with multiple levels of caching. Unlike previous optimal algorithms, these algorithms are cache oblivious: no variables dependent on hardware parameters, such as cache size and cache-line length, need to be tuned to achieve optimality. Nevertheless, these algorithms use an optimal amount of work and move data optimally among multiple levels of cache. For a cache with size M and cache-line length B where M = Ω(B2), the number of cache misses for an m × n matrix transpose is Θ(1 + mn/B). The number of cache misses for either an n-point FFT or the sorting of n numbers is Θ(1 + (n/B)(1 + logM n)). We also give a Θ(mnp)-work algorithm to multiply an m × n matrix by an n × p matrix that incurs Θ(1 + (mn + np + mp)/B + mnp/B√M) cache faults.We introduce an “ideal-cache” model to analyze our algorithms. We prove that an optimal cache-oblivious algorithm designed for two levels of memory is also optimal for multiple levels and that the assumption of optimal replacement in the ideal-cache model can be simulated efficiently by LRU replacement. We offer empirical evidence that cache-oblivious algorithms perform well in practice.read more
Citations
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Proceedings ArticleDOI
Parallel Integer Polynomial Multiplication
TL;DR: A new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures, and demonstrating the advantages of this new approach is proposed.
Journal ArticleDOI
Scientific computations on multi-core systems using different programming frameworks
TL;DR: The qualitative results show that the OpenMP, Cilk Plus, TBB, and SWARM frameworks require minimal programming effort, whereas the other models require advanced programming skills and experience, and general conclusions regarding the programming models and matrix operations for some parameters were obtained.
Proceedings ArticleDOI
Bounding Cache Miss Costs of Multithreaded Computations Under General Schedulers: Extended Abstract
Richard Cole,Vijaya Ramachandran +1 more
TL;DR: In this paper, the caching overhead incurred by a class of multithreaded algorithms when scheduled by an arbitrary scheduler was analyzed, and bounds that match or improve upon the well-known O(Q+S · (M/B)) caching cost for the randomized work stealing (RWS) scheduler were obtained.
Book ChapterDOI
I/O-Efficient Range Minima Queries
Peyman Afshani,Nodari Sitchinava +1 more
TL;DR: This paper studies the offline (batched) range minima query (RMQ) problem in the external memory (EM) and cache-oblivious (CO) models.
Book ChapterDOI
A paradigm for parallel matrix algorithms: scalable cholesky
TL;DR: A style for programming problems from matrix algebra is developed with a familiar example and new tools, yielding high performance with a couple of surprising exceptions.
References
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Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Journal ArticleDOI
An algorithm for the machine calculation of complex Fourier series
J.W. Cooley,John W. Tukey +1 more
TL;DR: Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Book
Computer Architecture: A Quantitative Approach
TL;DR: This best-selling title, considered for over a decade to be essential reading for every serious student and practitioner of computer design, has been updated throughout to address the most important trends facing computer designers today.