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A Tight Competitive Ratio for Online Submodular Welfare Maximization

Authors Amit Ganz, Pranav Nuti, Roy Schwartz

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  • Theory of computation → Online algorithms
Keywords
  • Online Algorithms
  • Submodular Maximization
  • Welfare Maximization
  • Approximation Algorithms

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Abstract

In this paper we consider the online Submodular Welfare (SW) problem. In this problem we are given n bidders each equipped with a general non-negative (not necessarily monotone) submodular utility and m items that arrive online. The goal is to assign each item, once it arrives, to a bidder or discard it, while maximizing the sum of utilities. When an adversary determines the items' arrival order we present a simple randomized algorithm that achieves a tight competitive ratio of 1/4. The algorithm is a specialization of an algorithm due to [Harshaw-Kazemi-Feldman-Karbasi MOR`22], who presented the previously best known competitive ratio of 3-2√2≈ 0.171573 to the problem. When the items' arrival order is uniformly random, we present a competitive ratio of ≈ 0.27493, improving the previously known 1/4 guarantee. Our approach for the latter result is based on a better analysis of the (offline) Residual Random Greedy (RRG) algorithm of [Buchbinder-Feldman-Naor-Schwartz SODA`14], which we believe might be of independent interest.

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Amit Ganz, Pranav Nuti, and Roy Schwartz. A Tight Competitive Ratio for Online Submodular Welfare Maximization. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 52:1-52:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ESA.2023.52

Author Details

Amit Ganz
  • The Henry and Marilyn Taub Faculty of Computer Science, Technion, Haifa, Israel
Pranav Nuti
  • Department of Computer Science, Stanford University, CA, USA
Roy Schwartz
  • The Henry and Marilyn Taub Faculty of Computer Science, Technion, Haifa, Israel

Funding

Amit Ganz and Roy Schwartz have received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement no. 852870-ERC-SUBMODULAR.

Acknowledgements

The authors would like to thank the anonymous referees for helpful remarks.

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