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Fault-Tolerant Approximate Distance Oracles with a Source Set

Authors Dipan Dey , Telikepalli Kavitha

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LIPIcs.FSTTCS.2025.27.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Weighted graphs
  • approximate distances
  • fault-tolerant data structures

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Abstract

Our input is an undirected weighted graph G = (V,E) on n vertices along with a source set S ⊆ V. The problem is to preprocess G and build a compact data structure such that upon query Qu(s,v,f) where (s,v) ∈ S×V and f is any faulty edge, we can quickly find a good estimate (i.e., within a small multiplicative stretch) of the s-v distance in G-f. We use a fault-tolerant ST-distance oracle from the work of Bilò et al. (STACS 2018) to construct an S×V approximate distance oracle or sourcewise approximate distance oracle of size Õ(|S|n + n^{3/2}) with multiplicative stretch at most 5. We construct another fault-tolerant sourcewise approximate distance oracle of size Õ(|S|n + n^{4/3}) with multiplicative stretch at most 13. Both the oracles have O(1) query answering time.

Cite As Get BibTex

Dipan Dey and Telikepalli Kavitha. Fault-Tolerant Approximate Distance Oracles with a Source Set. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.FSTTCS.2025.27

Author Details

Dipan Dey
  • Tata Institute of Fundamental Research, Mumbai, India
Telikepalli Kavitha
  • Tata Institute of Fundamental Research, Mumbai, India

Funding

Supported by the Department of Atomic Energy, Government of India, under project no. RTI4001.

References

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