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Edge-Weighted Online Stochastic Matching Under Jaillet-Lu LP

Author Shuyi Yan

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LIPIcs.ICALP.2026.156.pdf
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ACM Subject Classification
  • Theory of computation → Online algorithms
  • Mathematics of computing → Graph algorithms
Keywords
  • Online stochastic matching

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Abstract

The online stochastic matching problem was introduced by [Feldman et al., 2009], together with the (1-1/e)-competitive Suggested Matching algorithm. In the most general edge-weighted setting, this ratio has not been improved for more than one decade, until recently [Yan, 2024] beat the 1-1/e bound and [Qiu et al., 2023] further improved it to 0.650. Both works measure the online competitiveness against the offline LP relaxation introduced by Jaillet and Lu [Jaillet and Lu, 2014]. The same LP has also played an important role in other settings as it is a natural choice for two-choice online algorithms.
In this paper, we prove an upper bound of 0.663 and a lower bound of 0.662 for edge-weighted online stochastic matching under Jaillet-Lu LP. We propose a simple hard instance and identify the optimal online algorithm for this specific instance which has a competitive ratio of < 0.663. Despite the simplicity of the instance, we then show that a near-optimal algorithm for it, which has a competitive ratio of > 0.662, can be generalized to work on all instances without any loss.
As our algorithm is generalized from a real near-optimal algorithm instead of manually combining trivial strategies, it has two natural advantages compared with previous works: (1) its matching strategy varies from time to time; (2) it utilizes global information about offline vertices. On the other hand, the upper bound suggests that more powerful LPs and multiple-choice strategies are needed if we want to further improve the ratio by > 0.001.
In addition to our main result, we also generalize the asymptotic equivalence between the Poisson arrival model and the original online stochastic matching established by [Huang and Shu, 2021], removing the requirement of approximate monotonicity for the online algorithm.

Cite As Get BibTex

Shuyi Yan. Edge-Weighted Online Stochastic Matching Under Jaillet-Lu LP. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 156:1-156:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.156

Author Details

Shuyi Yan
  • University of Copenhagen, Denmark

Funding

  • Yan, Shuyi: Supported by VILLUM Foundation Grant 54451, Basic Algorithms Research Copenhagen (BARC).

Acknowledgements

We thank Mikkel Thorup and the anonymous reviewers for helpful comments.

References

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