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Parameterized Streaming Algorithms for Topological Sorting

Authors Ho-Lin Chen , Peng-Ting Lin , Meng-Tsung Tsai

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Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • Independence Number
  • Chain Cover
  • SCC Decomposition
  • 2-Satisfiability

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Abstract

Computing a topological ordering for an n-node directed acyclic graph (DAG) G is computationally challenging in streaming models. Chakrabarti et al. {[}SODA 2020{]} showed that in the insertion-only streaming model, every single-pass algorithm requires Ω(n²) space, and every k-pass algorithm requires n^{1+Ω(1/k)} space for any constant k ≥ 1. 
We study the parameterized complexity of streaming algorithms for topological sorting, considering two parameters: the independence number α and the maximum displacement δ. Our results include an O(1/ε)-pass O(α n^{1+ε})-space streaming algorithm and an O(n^{1/2})-pass O(n+δ²)-space streaming algorithm. For dense random DAGs, both α and δ are small, allowing us to improve the state-of-the-art for topological sorting in random DAGs.
As applications, we show that strongly connected components (SCC) decomposition and 2-satisfiability (2-SAT) can be solved in O(1/ε) passes using O(α n^{1+ε}) space and O(α_I n^{1+ε}) space, respectively, where α_I denotes the independence number of the implication graph induced by the input 2-SAT instance.

Cite As Get BibTex

Ho-Lin Chen, Peng-Ting Lin, and Meng-Tsung Tsai. Parameterized Streaming Algorithms for Topological Sorting. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.WADS.2025.18

Author Details

Ho-Lin Chen
  • National Taiwan University, Taipei, Taiwan
Peng-Ting Lin
  • Academia Sinica, Taipei, Taiwan
Meng-Tsung Tsai
  • Academia Sinica, Taipei, Taiwan

Funding

This research was supported in part by the National Science and Technology Council under contract NSTC 114-2221-E-001-023 and 113-2221-E-002-204-MY3.

Acknowledgements

We want to thank the anonymous reviewers for their valuable comments.

References

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