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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Proceedings ArticleDOI
POSTER: Cache-Oblivious MPI All-to-All Communications on Many-Core Architectures
TL;DR: This work proposes cache-oblivious algorithms for MPI all-to-all operations, in which data blocks are copied into the receive buffers in order to exploit data locality.
Proceedings ArticleDOI
Pipelined memory hierarchies: scalable organizations and application performance
Bilardi,Ekanadham,Pattnaik +2 more
TL;DR: In this paper, the authors propose memory organizations with the ability to accept requests at a constant rate without significantly affecting the latency of individual requests, which is within a constant factor of the minimum value achievable under fundamental physical constraints.
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Dynamic data replacement and adaptive scheduling policies in spark
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Proceedings ArticleDOI
GPU Performance Enhancement via Communication Cost Reduction: Case Studies of Radix Sort and WSN Relay Node Placement Problem
TL;DR: This study investigates two techniques, data streaming and data compression, to reduce the communication cost on GPU, and demonstrates the effectiveness of the two techniques via two case studies: radix sort and 3-star, a deployment algorithm in wireless sensor networks.
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.