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A New Impossibility Result for Online Bipartite Matching Problems

Authors Flavio Chierichetti , Mirko Giacchini , Alessandro Panconesi , Andrea Vattani

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  • Theory of computation → Online algorithms
Keywords
  • Bipartite Matching
  • Random Graphs
  • Competitive Ratio

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Abstract

Online Bipartite Matching with random user arrival is a fundamental problem in the online advertisement ecosystem. Over the last 30 years, many algorithms and impossibility results have been developed for this problem. In particular, the latest impossibility result was established by Manshadi, Oveis Gharan and Saberi [Manshadi et al., 2011] in 2011. Since then, several algorithms have been published in an effort to narrow the gap between the upper and the lower bounds on the competitive ratio.

In this paper we show that no algorithm can achieve a competitive ratio better than 1- e/(e^e) = 0.82062…, improving upon the 0.823 upper bound presented in [Manshadi et al., 2011]. Our construction is simple to state, accompanied by a fully analytic proof, and yields a competitive ratio bound intriguingly similar to 1 - 1/e, the optimal competitive ratio for the fully adversarial Online Bipartite Matching problem. 

Although the tightness of our upper bound remains an open question, we show that our construction is extremal in a natural class of instances.

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Flavio Chierichetti, Mirko Giacchini, Alessandro Panconesi, and Andrea Vattani. A New Impossibility Result for Online Bipartite Matching Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 58:1-58:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.58

Author Details

Flavio Chierichetti
  • Sapienza University of Rome, Italy
Mirko Giacchini
  • Sapienza University of Rome, Italy
Alessandro Panconesi
  • Sapienza University of Rome, Italy
Andrea Vattani
  • Reddit, San Francisco, CA, US

Funding

Flavio Chierichetti, Mirko Giacchini, and Alessandro Panconesi were supported in part by a Google Focused Research Award, by BiCi - Bertinoro international Center for informatics, and by the PRIN project 20229BCXNW funded by the European Union - Next Generation EU, Mission 4 Component 1, CUP B53D23012910006.

Acknowledgements

We thank Will Ma, David Wajc, Pan Xu, and the anonymous reviewers for several comments and suggestions.

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