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Communication Dans Un Congrès Année : 2024

Tightening I/O Lower Bounds through the Hourglass Dependency Pattern

Résumé

When designing an algorithm, one cares about arithmetic/computational complexity, but data movement (I/O) complexity plays an increasingly important role that highly impacts performance and energy consumption. For a given algorithm and a given I/O model, scheduling strategies such as loop tiling can reduce the required I/O down to a limit, called the I/O complexity, inherent to the algorithm itself. The objective of I/O complexity analysis is to compute, for a given program, its minimal I/O requirement among all valid schedules. We consider a sequential execution model with two memories, an infinite one, and a small one of size S on which the computations retrieve and produce data. The I/O is the number of reads and writes between the two memories. We identify a common “hourglass pattern” in the dependency graphs of several common linear algebra kernels. Using the properties of this pattern, we mathematically prove tighter lower bounds on their I/O complexity, which improves the previous state-of-the-art bound by a parametric ratio. This proof was integrated inside the IOLB automatic lower bound derivation tool.
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hal-04555744 , version 1 (23-04-2024)

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  • HAL Id : hal-04555744 , version 1

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Lionel Eyraud-Dubois, Guillaume Iooss, Julien Langou, Fabrice Rastello. Tightening I/O Lower Bounds through the Hourglass Dependency Pattern. SPAA 2024 - 36th ACM Symposium on Parallelism in Algorithms and Architectures, Jun 2024, Nantes, France. ⟨hal-04555744⟩
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