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DOI: 10.4230/LIPIcs.ICALP.2025.58

A New Impossibility Result for Online Bipartite Matching Problems

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

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

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)

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@InProceedings{chierichetti_et_al:LIPIcs.ICALP.2025.58,
  author =	{Chierichetti, Flavio and Giacchini, Mirko and Panconesi, Alessandro and Vattani, Andrea},
  title =	{{A New Impossibility Result for Online Bipartite Matching Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{58:1--58:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.58},
  URN =		{urn:nbn:de:0030-drops-234354},
  doi =		{10.4230/LIPIcs.ICALP.2025.58},
  annote =	{Keywords: Bipartite Matching, Random Graphs, Competitive Ratio}
}

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A New Impossibility Result for Online Bipartite Matching Problems

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