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Near-Optimal Vertex Fault-Tolerant Labels for Steiner Connectivity

Authors Koustav Bhanja , Asaf Petruschka

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ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Distributed algorithms
Keywords
  • Fault Tolerance
  • Labeling Schemes
  • Steiner Connectivity

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Abstract

We present a compact labeling scheme for determining whether a designated set of terminals in a graph remains connected after any f (or less) vertex failures occur. An f-FT Steiner connectivity labeling scheme for an n-vertex graph G = (V,E) with terminal set U ⊆ V provides labels to the vertices of G, such that given only the labels of any subset F ⊆ V with |F| ≤ f, one can determine if U remains connected in G-F. The main complexity measure is the maximum label length.
The special case U = V of global connectivity has been recently studied by Jiang, Parter, and Petruschka [Yonggang Jiang et al., 2025], who provided labels of n^{1-1/f} ⋅ poly(f,log n) bits. This is near-optimal (up to poly(f,log n) factors) by a lower bound of Long, Pettie and Saranurak [Yaowei Long et al., 2025]. Our scheme achieves labels of |U|^{1-1/f} ⋅ poly(f, log n) for general U ⊆ V, which is near-optimal for any given size |U| of the terminal set. To handle terminal sets, our approach differs from [Yonggang Jiang et al., 2025]. We use a well-structured Steiner tree for U produced by a decomposition theorem of Duan and Pettie [Ran Duan and Seth Pettie, 2020], and bypass the need for Nagamochi-Ibaraki sparsification [Hiroshi Nagamochi and Toshihide Ibaraki, 1992].

Cite As Get BibTex

Koustav Bhanja and Asaf Petruschka. Near-Optimal Vertex Fault-Tolerant Labels for Steiner Connectivity. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 44:1-44:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.44

Author Details

Koustav Bhanja
  • Weizmann Institute of Science, Rehovot, Israel
Asaf Petruschka
  • Weizmann Institute of Science, Rehovot, Israel

Funding

  • Bhanja, Koustav: Supported by Merav Parter’s European Research Council (ERC) grant under the European Union’s Horizon 2020 research and innovation programme, grant agreement No. 949083.
  • Petruschka, Asaf: Supported by an Azrieli Foundation fellowship, and by Merav Parter’s European Research Council (ERC) grant under the European Union’s Horizon 2020 research and innovation programme, grant agreement No. 949083.

Acknowledgements

We are thankful to Merav Parter for encouraging this collaboration and for valuable discussions.

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