DARTS.9.1.3.pdf
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Isospeed: Improving (min,+) Convolution by Exploiting (min,+)/(max,+) Isomorphism (Artifact)
Authors
Raffaele Zippo 
,
Paul Nikolaus ,
Giovanni Stea
-
Part of:
Issue:
Special Issue of the 35th Euromicro Conference on Real-Time Systems (ECRTS 2023)
Volume: DARTS, Volume 9 (ECOOP 2023)
Conference: Euromicro Conference on Real-Time Systems (ECRTS)
Journal: Dagstuhl Artifacts Series (DARTS) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-07-03
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Author Details
- 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
Acknowledgements
This work is inspired by the results [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.
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Raffaele Zippo, Paul Nikolaus, and Giovanni Stea. Isospeed: Improving (min,+) Convolution by Exploiting (min,+)/(max,+) Isomorphism (Artifact). In Special Issue of the 35th Euromicro Conference on Real-Time Systems (ECRTS 2023). Dagstuhl Artifacts Series (DARTS), Volume 9, Issue 1, pp. 3:1-3:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/DARTS.9.1.3
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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 abate the computation times of (min,+) convolution by orders of magnitude.
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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References
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Anne Bouillard, Marc Boyer, and Euriell Le Corronc. Deterministic Network Calculus: From Theory to Practical Implementation. Wiley, Hoboken, NJ, 2018.
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Victor Pollex, Henrik Lipskoch, Frank Slomka, and Steffen Kollmann. Runtime Improved Computation of Path Latencies with the Real-Time Calculus. In Proceedings of the 1st International Workshop on Worst-Case Traversal Time, pages 58-65, 2011.
- 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), volume 262 of Leibniz International Proceedings in Informatics (LIPIcs), pages 12:1-12:24. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPIcs.ECRTS.2023.12.
- Raffaele Zippo and Giovanni Stea. Nancy: An efficient parallel Network Calculus library. SoftwareX, 19:101178, 2022. URL: https://doi.org/10.1016/j.softx.2022.101178.