Fault-Tolerant ST-Diameter Oracles

Davide Bilò*, Keerti Choudhary*, Sarel Cohen*, Tobias Friedrich*, Simon Krogmann*, Martin Schirneck*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study the problem of estimating the ST-diameter of a graph that is subject to a bounded number of edge failures. An f-edge fault-tolerant ST-diameter oracle (f-FDO-ST) is a data structure that preprocesses a given graph G, two sets of vertices S, T, and positive integer f. When queried with a set F of at most f edges, the oracle returns an estimate Db of the ST-diameter diam(G−F, S, T), the maximum distance between vertices in S and T in G− F. The oracle has stretch σ ≥ 1 if diam(G−F, S, T) ≤ Db ≤ σ diam(G−F, S, T). If S and T both contain all vertices, the data structure is called an f-edge fault-tolerant diameter oracle (f-FDO). An f-edge fault-tolerant distance sensitivity oracles (f-DSO) estimates the pairwise graph distances under up to f failures. We design new f-FDOs and f-FDO-STs by reducing their construction to that of all-pairs and single-source f-DSOs. We obtain several new tradeoffs between the size of the data structure, stretch guarantee, query and preprocessing times for diameter oracles by combining our black-box reductions with known results from the literature. We also provide an information-theoretic lower bound on the space requirement of approximate f-FDOs. We show that there exists a family of graphs for which any f-FDO with sensitivity f ≥ 2 and stretch less than 5/3 requires Ω(n3/2) bits of space, regardless of the query time.

Original languageEnglish
Title of host publication50th International Colloquium on Automata, Languages, and Programming, ICALP 2023
EditorsKousha Etessami, Uriel Feige, Gabriele Puppis
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772785
StatePublished - Jul 2023
Externally publishedYes
Event50th International Colloquium on Automata, Languages, and Programming, ICALP 2023 - Paderborn, Germany
Duration: 10 Jul 202314 Jul 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference50th International Colloquium on Automata, Languages, and Programming, ICALP 2023


  • diameter oracles
  • distance sensitivity oracles
  • fault-tolerant data structures
  • space lower bounds


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