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Isospeed: Improving (min,+) Convolution by Exploiting (min,+)/(max,+) Isomorphism

Authors Raffaele Zippo , Paul Nikolaus , Giovanni Stea

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Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
  • Networks → Network performance analysis
  • Mathematics of computing → Mathematical software performance
Keywords
  • Deterministic Network Calculus
  • min-plus algebra
  • max-plus algebra
  • performance
  • algorithms

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Abstract

(min,+) convolution is the key operation in (min,+) algebra, a theory often used to compute performance bounds in real-time systems. As already observed in many works, its algorithm can be computationally expensive, due to the fact that: i) its complexity is superquadratic with respect to the size of the operands; ii) operands must be extended before starting its computation, and iii) said extension is tied to the least common multiple of the operand periods. 
In this paper, we leverage the isomorphism between (min,+) and (max,+) algebras to devise a new algorithm for (min,+) convolution, in which the need for operand extension is minimized. This algorithm is considerably faster than the ones known so far, and it allows us to reduce the computation times of (min,+) convolution by orders of magnitude.

Cite As Get BibTex

Raffaele Zippo, Paul Nikolaus, and Giovanni Stea. Isospeed: Improving (min,+) Convolution by Exploiting (min,+)/(max,+) Isomorphism. In 35th Euromicro Conference on Real-Time Systems (ECRTS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 262, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ECRTS.2023.12

Author Details

Raffaele Zippo
  • Dipartimento di Ingegneria dell'Informazione, University of Firenze, Italy
  • Dipartimento di Ingegneria dell'Informazione, University of Pisa, Italy
  • Distributed Computer Systems Lab (DISCO), TU Kaiserslautern, Germany
Paul Nikolaus
  • Distributed Computer Systems Lab (DISCO), TU Kaiserslautern, Germany
Giovanni Stea
  • Dipartimento di Ingegneria dell'Informazione, University of Pisa, Italy

Funding

This work was supported in part by the Italian Ministry of Education and Research (MIUR) in the framework of the FoReLab project (Departments of Excellence).

Acknowledgements

This work is inspired by the results in [Pollex et al., 2011] - we wish to thank Steffen Bondorf for pointing out this paper to us, as well as Raul-Paul Epure for suggestions with respect to some proofs.

Supplementary Materials

References

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