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Atomic Power in Forks: A Super-Logarithmic Lower Bound for Implementing Butterfly Networks in the Nonatomic Binary Fork-Join Model

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We prove an Ω (log n log log n) lower bound for the span of implementing the n input, log n-depth FFT circuit (also known as butterfly network) in the nonatomic binary fork-join model. In this model, memory-access synchronizations occur only through fork operations, which spawn two child threads, and join operations, which resume a parent thread when its child threads terminate. Our bound is asymptotically tight for the nonatomic binary fork-join model, which has been of interest of late, due to its conceptual elegance and ability to capture asynchrony. Our bound implies super-logarithmic lower bound in the nonatomic binary fork-join model for implementing the butterfly merging networks used, e.g., in Batcher's bitonic and odd-even mergesort networks. This lower bound also implies an asymptotic separation result for the atomic and nonatomic versions of the fork-join model, since, as we point out, FFT circuits can be implemented in the atomic binary fork-join model with span equal to their circuit depth.
Original languageEnglish
Title of host publicationProceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA)
Number of pages13
PublisherSociety for Industrial and Applied Mathematics
Publication date14 Jan 2021
Pages2141-2153
DOIs
Publication statusPublished - 14 Jan 2021
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    Research areas

  • lower bound, parallel computation, fork-join model

ID: 86579650