What does this research mean for the field?

The proposed randomized algorithm for finding an α-approximate minimum vertex cover in dynamic graph streams uses O(n²/α²) bits of space, achieving optimal space complexity. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to optimize space complexity when finding an α-approximate minimum vertex cover in dynamic graph streams.

March 16, 2026Open Access

Space Optimal Vertex Cover in Dynamic Streams

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The aim is to optimize space complexity when finding an α-approximate minimum vertex cover in dynamic graph streams.
Developed a randomized algorithm for αMVC using O(n²/α²) bits of space.
Identified 'easy' instances of the problem through random greedy matching.
Exploited sparse induced subgraphs to achieve space savings on 'hard' instances.
Achieved optimal space complexity matching existing lower bounds up to constant factors.
Showed that the proposed method efficiently returns the entire vertex set for easy problems.
Highlighted unresolved space complexity issues for other dynamic graph streaming problems.

Authors

KNKheeran K. Naidu VSVihan ShahUniversity of Waterloo

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Implication

Randomized algorithm approximates minimum vertex cover in dynamic graphs, highlighting space efficiency implications.

Cite This Study

Naidu et al. (2022) studied this question.

synapsesocial.com/papers/69b79e6e8166e15b153abc4b https://doi.org/10.4230/lipics.approx/random.2022.53

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Space Optimal Vertex Cover in Dynamic Streams

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Discussion

Implication

Cite This Study

Space Optimal Vertex Cover in Dynamic Streams

Key Points

Discussion

Implication

Cite This Study

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