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Vertex Sparsification for Edge Connectivity in Polynomial Time

Author Yang P. Liu

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Author Details

Yang P. Liu
  • Department of Mathematics, Stanford University, CA, USA

Funding

This work was supported by the NDSEG Fellowship and the Google Research Fellowship.

Acknowledgements

The author would like to thank Yunbum Kook for feedback on an earlier version of this manuscript, anonymous reviewers for feedback to improve the presentation of this paper, and Richard Peng for useful discussions and encouragement.

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Yang P. Liu. Vertex Sparsification for Edge Connectivity in Polynomial Time. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 83:1-83:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ITCS.2023.83

Abstract

An important open question in the area of vertex sparsification is whether (1+ε)-approximate cut-preserving vertex sparsifiers with size close to the number of terminals exist. The work [Parinya Chalermsook et al., 2021] (SODA 2021) introduced a relaxation called connectivity-c mimicking networks, which asks to construct a vertex sparsifier which preserves connectivity among k terminals exactly up to the value of c, and showed applications to dynamic connectivity data structures and survivable network design. We show that connectivity-c mimicking networks with Õ(kc³) edges exist and can be constructed in polynomial time in n and c, improving over the results of [Parinya Chalermsook et al., 2021] for any c ≥ log n, whose runtimes depended exponentially on c.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Paths and connectivity problems
Keywords
  • Vertex-sparsification
  • edge-connectivity
  • Gammoids

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