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The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization

Authors Zhiyi Huang , Chui Shan Lee , Xinkai Shu , Zhaozi Wang

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ACM Subject Classification
  • Theory of computation → Online algorithms
Keywords
  • Online Algorithms
  • Fair Division
  • Nash Welfare

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Abstract

We study the online allocation of divisible items to n agents with additive valuations for p-mean welfare maximization, a problem introduced by Barman, Khan, and Maiti (2022). Our algorithmic and hardness results characterize the optimal competitive ratios for the entire spectrum of -∞ ≤ p ≤ 1. Surprisingly, our improved algorithms for all p ≤ (1)/(log n) are simply the greedy algorithm for the Nash welfare, supplemented with two auxiliary components to ensure all agents have non-zero utilities and to help a small number of agents with low utilities. In this sense, the long arm of Nashian allocation achieves near-optimal competitive ratios not only for Nash welfare but also all the way to egalitarian welfare.

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Zhiyi Huang, Chui Shan Lee, Xinkai Shu, and Zhaozi Wang. The Long Arm of Nashian Allocation in Online p-Mean Welfare Maximization. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 98:1-98:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.98

Author Details

Zhiyi Huang
  • The University of Hong Kong, Pokfulam, Hong Kong
Chui Shan Lee
  • The University of Hong Kong, Pokfulam, Hong Kong
Xinkai Shu
  • Max Planck Institute for Informatics, Saarbrücken, Germany
Zhaozi Wang
  • New York University, NY, US

Funding

  • Huang, Zhiyi: This work is supported by NSFC (No. 6212290003).

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