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
More filters
Book ChapterDOI
Cache Oblivious Distribution Sweeping
TL;DR: This work adapts the distribution sweeping model for divide-and-conquer algorithms to the cache oblivious model, and demonstrates by a series of algorithms the feasibility of the method in a cache oblivious setting.
HAT-trie: a cache-conscious trie-based data structure for strings
Nikolas Askitis,Ranjan Sinha +1 more
TL;DR: The HAT-trie is shown to be the most efficient trie-based data structure for managing variable-length strings in-memory while maintaining sort order and approaching that of the cache-conscious hash table.
Journal ArticleDOI
Oblivious algorithms for multicores and networks of processors
TL;DR: This work introduces a multicore-oblivious (MO) approach to algorithms and schedulers for HM, and presents efficient MO algorithms for several fundamental problems including matrix transposition, FFT, sorting, the Gaussian Elimination Paradigm, list ranking, and connected components.
Proceedings ArticleDOI
Oblivious algorithms for multicores and network of processors
TL;DR: This work introduces a multicore-oblivious (MO) approach to algorithms and schedulers for HM, and presents efficient MO algorithms for several fundamental problems including matrix transposition, FFT, sorting, the Gaussian Elimination Paradigm, list ranking, and connected components.
Proceedings ArticleDOI
The input/output complexity of triangle enumeration
Rasmus Pagh,Francesco Silvestri +1 more
TL;DR: The algorithm is cache-oblivious and also I/O optimal, and it is shown that any algorithm enumerating t distinct triangles must always use Ω(√MB) I/Os, and there are graphs for which t=Ω(E3/2).
References
More filters
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.