@inproceedings{1e84bff1a3c848ff97324ca4ae5a24f4,
title = "Removing the log Factor from (min, +)-Products on Bounded Range Integer Matrices",
abstract = "We revisit the problem of multiplying two square matrices over the (min, +) semi-ring, where all entries are integers from a bounded range [−M: M] ∪ {∞}. The current state of the art for this problem is a simple O(Mnω log M) time algorithm by Alon, Galil and Margalit [JCSS'97], where ω is the exponent in the runtime of the fastest matrix multiplication (FMM) algorithm. We design a new simple algorithm whose runtime is O(Mnω + Mn2 log M), thereby removing the log M factor in the runtime if ω > 2 or if nω = Ω(n2 log n).",
keywords = "(min, +)-product, FFT, FMM",
author = "Dvir Fried and Tsvi Kopelowitz and Ely Porat",
note = "Publisher Copyright: {\textcopyright} Dvir Fried, Tsvi Kopelowitz, and Ely Porat; licensed under Creative Commons License CC-BY 4.0.; 32nd Annual European Symposium on Algorithms, ESA 2024 ; Conference date: 02-09-2024 Through 04-09-2024",
year = "2024",
month = sep,
doi = "https://doi.org/10.4230/LIPIcs.ESA.2024.57",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Timothy Chan and Johannes Fischer and John Iacono and Grzegorz Herman",
booktitle = "32nd Annual European Symposium on Algorithms, ESA 2024",
address = "ألمانيا",
}