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Approximate Single Source Dual Fault Tolerant Distance Oracle

Authors Koustav Das , Manoj Gupta

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Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Shortest paths
  • Theory of computation → Data structures design and analysis
Keywords
  • Fault-tolerant distance oracle
  • Shortest paths
  • Graph algorithms
  • Dual failures
  • Approximate distance oracle

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Abstract

We are given an undirected weighted graph G with n vertices and m edges, edge weights in [1, W], and a designated source vertex s. We design a single source dual fault tolerant distance oracle for G. Given a destination vertex t and a set F of at most two faulty edges, the oracle returns a (1 + O(ε))-approximation of the weight of the shortest path from the source s to t avoiding F. Our oracle uses Õ(n√n) space and has Õ(1) query time.
Prior to our result, single source single fault tolerant oracles were known to return a (1+ε) approximation of the weight of the shortest path using Õ(n) space and O(1) query time. However, extending these approaches to multiple faults remained an open problem. Indeed, all (1+ε)-approximate distance oracles that handle multiple faults require Ω(n²) space. We break this bound by presenting the first dual fault tolerant distance oracle with o(n²) space.

Cite As Get BibTex

Koustav Das and Manoj Gupta. Approximate Single Source Dual Fault Tolerant Distance Oracle. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 90:1-90:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.90

Author Details

Koustav Das
  • Department of Computer Science and Engineering, IIT Gandhinagar, India
Manoj Gupta
  • Department of Computer Science and Engineering, IIT Gandhinagar, India

Funding

  • Gupta, Manoj: Supported by ANRF grant ANRF/ARGM/2025/001853/MTR

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