Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deterministic Sensitivity Oracles for Diameter, Eccentricities and All
  Pairs Distances   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.

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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th