October 19, 2025Open Access

Dynamic Approximate Maximum Matching in the Distributed Vertex Partition Model

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The randomized Las Vegas algorithm achieves an expected update time of O(√m/βk) rounds for maintaining a 2/3-approximate maximum matching.
Any algorithm requires a worst-case update time of Ω(n/βk² log n) rounds when maintaining a maximal matching without 3-augmenting paths.
A randomized algorithm maintains a 2/3-approximate maximum matching with a worst-case update time of Ω(ℓ log n/√(βk)) rounds for batch-dynamic updates.
Lower bounds indicate Ω(ℓ/βk log n) for maintaining maximal matching under certain conditions, highlighting algorithmic challenges.

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Implication

Analysis shows high probability in maintaining approximate maximum matching in dynamic graph settings, indicating the complexity of algorithmic adaptation.

Cite This Study

Robinson et al. (2025) studied this question.

synapsesocial.com/papers/68f4c985d9958eec2a573d0d https://doi.org/10.48550/arxiv.2504.17338

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Implication

Analysis shows high probability in maintaining approximate maximum matching in dynamic graph settings, indicating the complexity of algorithmic adaptation.

Dynamic Approximate Maximum Matching in the Distributed Vertex Partition Model

Key Points

Discussion

Implication

Cite This Study

Dynamic Approximate Maximum Matching in the Distributed Vertex Partition Model

Key Points

Discussion

Implication

Cite This Study

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