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Connectivity Oracle Under Vertex Failures by Shortcutting Unbreakable Decomposition

Authors Xizhe Li , Yaowei Long , David Pidugu, Thatchaphol Saranurak , Benyu Wang

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LIPIcs.ICALP.2026.139.pdf
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ACM Subject Classification
  • Theory of computation → Data structures design and analysis
Keywords
  • Graphs
  • Fault tolerant
  • Oracles

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Abstract

We study connectivity oracle under vertex failures, one of the most fundamental graph data structures with many applications. We provide a new deterministic connectivity oracle that handles update in O(k⁶) time and answers query in O(k) time, while using 2^O(k²) n + O(k²n α_c(n)) space and k^O(k²) n + O(m + k³ n log² n + k⁶n log n) preprocessing time. 
Although some previous works achieve k² ⋅ n^o(1) update time and O(k) query time [Long and Saranurak, 2022; Yaowei Long and Yunfan Wang, 2024], the update time is still n-dependent, while oracles that have n-independent update and query times [Michal Pilipczuk et al., 2022; Jan van den Brand and Thatchaphol Saranurak, 2019] cannot achieve optimal O(k) query time [Monika Henzinger et al., 2015] and often have Ω(n²) space and processing time. Our solution would be the first vertex-failure connectivity oracle that achieves O(k) query time with update time completely independent of n, while improving space usage and having competitive preprocessing time.

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Xizhe Li, Yaowei Long, David Pidugu, Thatchaphol Saranurak, and Benyu Wang. Connectivity Oracle Under Vertex Failures by Shortcutting Unbreakable Decomposition. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 139:1-139:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.139

Author Details

Xizhe Li
  • University of Michigan, Ann Arbor, MI, USA
Yaowei Long
  • University of Michigan, Ann Arbor, MI, USA
David Pidugu
  • University of Michigan, Ann Arbor, MI, USA
Thatchaphol Saranurak
  • University of Michigan, Ann Arbor, MI, USA
Benyu Wang
  • University of Michigan, Ann Arbor, MI, USA

Funding

  • Saranurak, Thatchaphol: Supported by NSF Grant CCF-2238138 and a Sloan Fellowship.

References

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