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
Transforming loops to recursion for multi-level memory hierarchies
Qing Yi,Vikram Adve,Ken Kennedy +2 more
TL;DR: A new compiler transformation that can be used to convert loop nests into recursive form automatically is presented, and an improved algorithm for transitive dependence analysis is developed that is much faster than the best previously known algorithm in practice.
Proceedings ArticleDOI
Optimizing graph algorithms for improved cache performance
TL;DR: A cache-oblivious implementation of the Floyd-Warshall algorithm for the fundamental graph problem of all-pairs shortest paths is presented, which achieves the lower bound on processor-memory traffic of /spl Omega/(N/sup 3///spl radic/C), where N and C are the problem size and cache size.
Book ChapterDOI
Funnel Heap - A Cache Oblivious Priority Queue
TL;DR: An alternative optimal cache oblivious priority queue based only on binary merging is devised and it is shown that the structure can be made adaptive to different usage profiles.
Proceedings ArticleDOI
Executing task graphs using work-stealing
TL;DR: NABBIT is a work-stealing library for execution of task graphs with arbitrary dependencies which is implemented as a library for the multithreaded programming language Cilk++ is proved that Nabbit executes static task graphs in parallel in time which is asymptotically optimal for graphs whose nodes have constant in-degree and out-degree.
Book ChapterDOI
Exponential Structures for Efficient Cache-Oblivious Algorithms
TL;DR: A linear-space data structure for dynamic searching that supports searches and updates in optimal O(logB N) worst-case I/Os is given, eliminating amortization from the result of Bender, Demaine, and Farach-Colton (FOCS '00).
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.