@inproceedings{d4d519b0416d43e3a7e1dc985b615126,
title = "Minimizing I/O in Toom-Cook Algorithms",
abstract = "Long integer multiplication is a fundamental kernel in many linear algebra and cryptography computations. Toom-Cook-k (k∈N) are a family of fast long integer multiplication algorithms frequently used in many applications, particularly for small k sizes (2, 3, and 4). Previous studies focus on minimizing Toom-Cook{\textquoteright}s arithmetic cost, sometimes at the expense of asymptotically higher communication costs and memory footprint. For many high-performance computing applications, the bottleneck is communication rather than arithmetic. We propose new versions of Toom-Cook-k algorithms that simultaneously reduce their arithmetic cost, communication cost, and memory footprint. We obtain these results by utilizing the alternative basis and Toom-Graph techniques. The arithmetic costs of the new algorithms are only slightly higher than that of the best previous solution, while the communication costs and memory footprint are significantly reduced and proved to be optimal.",
keywords = "Alternative Basis Method, Bilinear Algorithms, Fast Long Integer Multiplication, I/O Complexity, Toom-Cook, Toom-Graph",
author = "Roy Nissim and Oded Schwartz and Yuval Spiizer",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 30th International Conference on Parallel and Distributed Computing, Euro-Par 2024 ; Conference date: 26-08-2024 Through 30-08-2024",
year = "2024",
language = "الإنجليزيّة",
isbn = "9783031695827",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "59--73",
editor = "Jesus Carretero and Javier Garcia-Blas and Sameer Shende and Ivona Brandic and Katzalin Olcoz and Martin Schreiber",
booktitle = "Euro-Par 2024",
address = "ألمانيا",
}