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Deterministic Independent Sets in the Semi-Streaming Model

Author Daniel Ye

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ACM Subject Classification
  • Theory of computation → Lower bounds and information complexity
Keywords
  • Sublinear Algorithms
  • Derandomization
  • Semi-Streaming Algorithms

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Abstract

We consider the independent set problem in the semi-streaming model. For any input graph G = (V, E) with n vertices, an independent set is a set of vertices with no edges between any two elements. In the semi-streaming model, G is presented as a stream of edges and any algorithm must use Õ(n) bits of memory to output a large independent set at the end of the stream.

Prior work has designed various semi-streaming algorithms for finding independent sets. Due to the hardness of finding maximum and maximal independent sets in the semi-streaming model, the focus has primarily been on finding independent sets in terms of certain parameters, such as the maximum degree Δ. In particular, there is a simple randomized algorithm that obtains independent sets of size n/(Δ+1) in expectation, which can also be achieved with high probability using more complicated algorithms. For deterministic algorithms, the best bounds are significantly weaker. The best we know is a straightforward algorithm that finds an Ω̃(n/(Δ²)) size independent set.

We show that this straightforward algorithm is nearly optimal by proving that any deterministic semi-streaming algorithm can only output an Õ(n/(Δ²)) size independent set. Our result proves a strong separation between the power of deterministic and randomized semi-streaming algorithms for the independent set problem.

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Daniel Ye. Deterministic Independent Sets in the Semi-Streaming Model. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 135:1-135:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICALP.2025.135

Author Details

Daniel Ye
  • University of Waterloo, Canada

Funding

Supported in part by Sepehr Assadi’s Sloan Research Fellowship and NSERC Discovery grant.

Acknowledgements

I would like to thank Sepehr Assadi for introducing me to this problem and for his numerous discussions, comments, and feedback throughout the development of this work. Without him, this would not have been possible. I would also like to thank Vihan Shah, Janani Sundaresan, and Christopher Trevisan for their insightful comments and meticulous remarks on earlier versions of this work.

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