Journal ArticleDOI
Cache-Oblivious Algorithms
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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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Journal ArticleDOI
I/O-efficient data structures for non-overlapping indexing
TL;DR: This work presents an O ( n log 2 n ) space data structure in the cache-aware model that can answer queries in optimal O ( m B + log B Ⅱ n + nocc [ s, e ] B ) I/O operations, where nocc is the output size.
Proceedings ArticleDOI
Balanced Partitioning of Several Cache-Oblivious Algorithms
TL;DR: PACO as discussed by the authors is a cache-oblivious algorithm for parallelizing Strassen's algorithm on an arbitrary number of processors in a shared-memory setting, and it can be extended to a distributed-memory architecture or a heterogeneous computing system.
Journal ArticleDOI
On Memory Traffic and Optimisations for Low-order Finite Element Assembly Algorithms on Multi-core CPUs
TL;DR:
Proceedings ArticleDOI
Balanced Dense Multivariate Multiplication: The General Case
TL;DR: In this paper , general preprocessing techniques are proposed to reshape dense multivariate polynomials over finite fields, in order to minimize the cost of memory accesses, while preserving sufficient parallelism, so as to reduce the running time of polynomial multiplication in multi-threaded implementations.
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.