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Fault-Tolerant ST-Diameter Oracles

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

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Author Details

Davide Bilò
  • Department of Information Engineering, Computer Science and Mathematics, University of L'Aquila, Italy
Keerti Choudhary
  • Department of Computer Science and Engineering, Indian Institute of Technology Delhi, India
Sarel Cohen
  • School of Computer Science, Tel-Aviv-Yaffo Academic College, Israel
Tobias Friedrich
  • Hasso Plattner Institute, Universität Potsdam, Germany
Simon Krogmann
  • Hasso Plattner Institute, Universität Potsdam, Germany
Martin Schirneck
  • Faculty of Computer Science, Universität Wien, Austria

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Davide Bilò, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, Simon Krogmann, and Martin Schirneck. Fault-Tolerant ST-Diameter Oracles. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ICALP.2023.24

Abstract

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 D̂ 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) ⩽ D̂ ⩽ 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(n^{3/2}) bits of space, regardless of the query time.

Subject Classification

ACM Subject Classification
  • Theory of computation → Shortest paths
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Cell probe models and lower bounds
Keywords
  • diameter oracles
  • distance sensitivity oracles
  • space lower bounds
  • fault-tolerant data structures

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