Abstract | ||
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Researchers and practitioners have for long worked on improving the computational complexity of algorithms, focusing on reducing the number of operations needed to perform a computation. However the hardware trend nowadays clearly shows a higher performance and energy cost for data movements than computations: quality algorithms have to minimize data movements as much as possible.
The theoretical operational complexity of an algorithm is a function of the total number of operations that must be executed, regardless of the order in which they will actually be executed. But theoretical data movement (or, I/O) complexity is fundamentally different: one must consider all possible legal schedules of the operations to determine the minimal number of data movements achievable, a major theoretical challenge. I/O complexity has been studied via complex manual proofs, e.g., refined from Ω(n3/√S) for matrix-multiply on a cache size S by Hong & Kung to 2n3/√S by Smith et al. While asymptotic complexity may be sufficient to compare I/O potential between broadly different algorithms, the accuracy of the reasoning depends on the tightness of these I/O lower bounds. Precisely, exposing constants is essential to enable precise comparison between different algorithms: for example the 2n3/√S lower bound allows to demonstrate the optimality of panel-panel tiling for matrix-multiplication.
We present the first static analysis to automatically derive non-asymptotic parametric expressions of data movement lower bounds with scaling constants, for arbitrary affine computations. Our approach is fully automatic, assisting algorithm designers to reason about I/O complexity and make educated decisions about algorithmic alternatives.
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Year | DOI | Venue |
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2020 | 10.1145/3385412.3385989 | PLDI '20: 41st ACM SIGPLAN International Conference on Programming Language Design and Implementation
London
UK
June, 2020 |
Keywords | DocType | ISBN |
Data access complexity, I/O lower bounds, Static analysis, Affine programs | Conference | 978-1-4503-7613-6 |
Citations | PageRank | References |
1 | 0.35 | 0 |
Authors | ||
5 |
Name | Order | Citations | PageRank |
---|---|---|---|
Olivry Auguste | 1 | 1 | 0.35 |
Langou Julien | 2 | 1 | 0.35 |
Louis-noël Pouchet | 3 | 880 | 47.61 |
P. Sadayappan | 4 | 4821 | 344.32 |
Fabrice Rastello | 5 | 482 | 38.30 |