Removing the log Factor from (min,+)-Products on Bounded Range Integer Matrices
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Removing the log Factor from (min,+)-Products on Bounded Range Integer Matrices

Authors Dvir Fried , Tsvi Kopelowitz , Ely Porat

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Author Details

Dvir Fried
  • Bar-Ilan University, Ramat-Gan, Israel
Tsvi Kopelowitz
  • Bar-Ilan University, Ramat-Gan, Israel
Ely Porat
  • Bar-Ilan University, Ramat-Gan, Israel

Funding

Supported by ISF grant no. 1926/19, by a BSF grant 2018364, and by an ERC grant MPM under the EU’s Horizon 2020 Research and Innovation Programme (grant no. 683064).

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Dvir Fried, Tsvi Kopelowitz, and Ely Porat. Removing the log Factor from (min,+)-Products on Bounded Range Integer Matrices. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 57:1-57:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.57

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(M n^{ω} 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(M n^ω + M n² log M), thereby removing the logM factor in the runtime if ω > 2 or if n^ω = Ω (n²log n).

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • FMM
  • (min
  • +)-product
  • FFT

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