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Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment

Authors Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, Seeun William Umboh

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Author Details

Tomer Ezra
  • Harvard University, Cambridge, MA, USA
Stefano Leonardi
  • Sapienza University of Rome, Italy
Michał Pawłowski
  • MIMUW, University of Warsaw, Poland
  • IDEAS NCBR, Warsaw, Poland
Matteo Russo
  • Sapienza University of Rome, Italy
Seeun William Umboh
  • School of Computing and Information Systems, The University of Melbourne, Australia
  • ARC Training Centre in Optimisation Technologies, Integrated Methodologies, and Applications (OPTIMA), Melbourne, Australia

Funding

  • Ezra, Tomer: Supported by the Harvard University Center of Mathematical Sciences and Applications.
  • Leonardi, Stefano: Supported by the ERC Advanced Grant 788893 AMDROMA and MIUR PRIN project ALGADIMAR.
  • Russo, Matteo: Supported by the ERC Advanced Grant 788893 AMDROMA and MIUR PRIN project ALGADIMAR.
  • Umboh, Seeun William: Part of this work was done when the author was visiting the Sapienza University of Rome, and at the School of Computer Science, University of Sydney.

Acknowledgements

We thank the anonymous reviewers for their valuable feedback.

Cite AsGet BibTex

Tomer Ezra, Stefano Leonardi, Michał Pawłowski, Matteo Russo, and Seeun William Umboh. Universal Optimization for Non-Clairvoyant Subadditive Joint Replenishment. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.12

Abstract

The online joint replenishment problem (JRP) is a fundamental problem in the area of online problems with delay. Over the last decade, several works have studied generalizations of JRP with different cost functions for servicing requests. Most prior works on JRP and its generalizations have focused on the clairvoyant setting. Recently, Touitou [Noam Touitou, 2023] developed a non-clairvoyant framework that provided an O(√{n log n}) upper bound for a wide class of generalized JRP, where n is the number of request types. We advance the study of non-clairvoyant algorithms by providing a simpler, modular framework that matches the competitive ratio established by Touitou for the same class of generalized JRP. Our key insight is to leverage universal algorithms for Set Cover to approximate arbitrary monotone subadditive functions using a simple class of functions termed disjoint. This allows us to reduce the problem to several independent instances of the TCP Acknowledgement problem, for which a simple 2-competitive non-clairvoyant algorithm is known. The modularity of our framework is a major advantage as it allows us to tailor the reduction to specific problems and obtain better competitive ratios. In particular, we obtain tight O(√n)-competitive algorithms for two significant problems: Multi-Level Aggregation and Weighted Symmetric Subadditive Joint Replenishment. We also show that, in contrast, Touitou’s algorithm is Ω(√{n log n})-competitive for both of these problems.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Set Cover
  • Joint Replenishment
  • TCP-Acknowledgment
  • Subadditive Function Approximation
  • Multi-Level Aggregation

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