License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2023.24
URN: urn:nbn:de:0030-drops-180762
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/18076/
Bilò, Davide ;
Choudhary, Keerti ;
Cohen, Sarel ;
Friedrich, Tobias ;
Krogmann, Simon ;
Schirneck, Martin
Fault-Tolerant ST-Diameter Oracles
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.
BibTeX - Entry
@InProceedings{bilo_et_al:LIPIcs.ICALP.2023.24,
author = {Bil\`{o}, Davide and Choudhary, Keerti and Cohen, Sarel and Friedrich, Tobias and Krogmann, Simon and Schirneck, Martin},
title = {{Fault-Tolerant ST-Diameter Oracles}},
booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
pages = {24:1--24:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-278-5},
ISSN = {1868-8969},
year = {2023},
volume = {261},
editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18076},
URN = {urn:nbn:de:0030-drops-180762},
doi = {10.4230/LIPIcs.ICALP.2023.24},
annote = {Keywords: diameter oracles, distance sensitivity oracles, space lower bounds, fault-tolerant data structures}
}
Keywords: |
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diameter oracles, distance sensitivity oracles, space lower bounds, fault-tolerant data structures |
Collection: |
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50th International Colloquium on Automata, Languages, and Programming (ICALP 2023) |
Issue Date: |
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2023 |
Date of publication: |
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05.07.2023 |