@inproceedings{ab410dba7160478b98172dca8e62b165,
title = "Deterministic Sensitivity Oracles for Diameter, Eccentricities and All Pairs Distances",
abstract = "We construct data structures for extremal and pairwise distances in directed graphs in the presence of transient edge failures. Henzinger et al. [ITCS 2017] initiated the study of fault-tolerant (sensitivity) oracles for the diameter and vertex eccentricities. We extend this with a special focus on space efficiency. We present several new data structures, among them the first fault-tolerant eccentricity oracle for dual failures in subcubic space. We further prove lower bounds that show limits to approximation vs. space and diameter vs. space trade-offs for fault-tolerant oracles. They highlight key differences between data structures for undirected and directed graphs. Initially, our oracles are randomized leaning on a sampling technique frequently used in sensitivity analysis. Building on the work of Alon, Chechik, and Cohen [ICALP 2019] as well as Karthik and Parter [SODA 2021], we develop a hierarchical framework to derandomize fault-tolerant data structures. We first apply it to our own diameter and eccentricity oracles and then show its versatility by derandomizing algorithms from the literature: the distance sensitivity oracle of Ren [JCSS 2022] and the Single-Source Replacement Path algorithm of Chechik and Magen [ICALP 2020]. This way, we obtain the first deterministic distance sensitivity oracle with subcubic preprocessing time.",
keywords = "derandomization, diameter, eccentricity, fault-tolerant data structure, sensitivity oracle, space lower bound",
author = "Davide Bil{\`o} and Keerti Choudhary and Sarel Cohen and Tobias Friedrich and Martin Schirneck",
note = "Publisher Copyright: {\textcopyright} Davide Bil{\`o}, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, and Martin Schirneck; licensed under Creative Commons License CC-BY 4.0; 49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022 ; Conference date: 04-07-2022 Through 08-07-2022",
year = "2022",
month = jul,
day = "1",
doi = "10.4230/LIPIcs.ICALP.2022.22",
language = "אנגלית",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Mikolaj Bojanczyk and Emanuela Merelli and Woodruff, {David P.}",
booktitle = "49th EATCS International Conference on Automata, Languages, and Programming, ICALP 2022",
}